Yuriy Drozd - Publications

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Books:

  1. (with V. V. Kirichenko) Higher Algebra. Kiev University, p.I, 1971, p.II, 1973.
  2. (with V. V. Kirichenko) Finite Dimensional Algebras. Vyshcha Shkola, Kiev, 1980 Download DJVU (Russian) (English enlarged edition: Springer-Verlag, 1994.)
  3. Galois Theory. Kiev University, 1997. Download PDF (Ukrainian)
  4. Theory of Algebraic Numbers, Kiev University, 1998. Download PDF (Ukrainian)
  5. Introduction to Algebraic Geometry. Klasyka Publishers, L'viv, 2004.
    Download PDF: English Ukrainian
  6. Basic Mathematical Logic. Kiev University, 2005. Download PDF (Ukrainian)
  7. Vector Bundles over Projective Curves. IMPA, Rio de Janeiro, 2008. (Ukrainian revised version: Inst. Math. NAS Ukraine, Kyiv, 2010). Download PDF Ukrainian version PDF
  8. (with I.Burban) Maximal Cohen-Macaulay Modules over Non-Isolated Surface Singularities. Memoirs AMS, v.248, No.1178, 2017.

Research Articles:

  1. Backström rings. Pac. J. Math. 323:1 (2023) 67-88. arXiv:2206.12875 [math.RT]
  2. (with A.Plakosh) Representations of Munn algebras and related semigroups. Commun. Algebra 51:3 (2023) 930-938. arXiv:2202.06103 [math.RT]
  3. (with A.Plakosh) Cohomologies of regular lattices over the Kleinian 4-group. J. Pure Abstract Algebra 227:2 (2023) Art.107178, 15 p. arXiv:2201.11833 [math.RT]
  4. On K0 of locally finite categories. J. Algebra 596 (2022) 289-310. arXiv:2005.14568 [math.RT]
  5. (with A.Plakosh) Chernikov 2-groups with Kleinian top and totally reduced bottom. . Ukr. Math. J. 73:7 (2021) 1005-1008.
  6. Rejection lemma and almost split sequences. Ukr. Math. J. 73:6 (2021) 780-798. arXiv:2004.01911 [math.RT]
  7. Matrix problems and representations of algebras. Zb. Pr. Inst. Mat. NAN Ukr. 17:2 (2020) 57-81.
  8. (with V.Gerasimenko, S.Maksymenko) 100 years of the Mathematical Institute of the Ukrainian Academy of Sciences. Zb. Pr. Inst. Mat. NAN Ukr. 17:2 (2020) 1-9.
  9. (with I.Burban) Morita theory for non-commutative Noetherian schemes. Adv. Math. 399 (2022) Art. 108273, 42 p.  arXiv:1911.01242 [math.AG]
  10. (with A.Plakosh) Cohomologies of Kleinian 4-group. Arch. Math. 115:2 (2020) 135-145. arXiv:1910.03868 [math.GR]
  11. (with O.Tovpyha) Cohen-Macaulay modules over the plane curve singularity of type T44, II. Algebra Discrete Math. 28:1 (2019) 75-93.
  12. (with O.Tovpyha) Cohen-Macaulay modules over the plane curve singularity of type T36. Algebra Discrete Math. 28:2 (2019) 213-233. (arXiv:1910.03859 [math.AC])
  13. (with I.Burban) Non-commutative nodal curves and derived tame algebras. arXiv:1805.05174 [math.AG]
  14. (with I.Burban and V.Gavran) Minors and resolutions of non-commutative schemes. Eur. J. Math, 3:2 (2017) 311-341. (arXiv:1501.06023 [math.AG])
  15. (with A.I.Plakosh) Cohomologies of finite abelian groups. Algebra Discrete Math. 24:1 (2017) 144-157. (arXiv:1709.05616 [math.Gr])
  16. (with I.Burban and V.Gavran) Minors and categorical resolutions. Singularities and Computer Algebra. Springer, 2017, 71-95.
  17. (with N.Golovashchuk and V.Zembyk) Representations of nodal algebras of type E. Algebra Discrete Math. 23:1 (2017) 16-34.
  18. (with O.Tovpyha) On Cohen-Macaulay modules over the plane curve singularity of type T44. Arch. Math. 108 (2017) 569-579 (arXiv:1610.05033 [math.AC])
  19. (with A.Plakosh) On nilpotent Chernikov 2-groups with elementary tops, Algebra Discrete Math.  22:2 (2016), 201-208 (arXiv:1610.05030 [math.GR])
  20. (with I.Burban and V.Gavran) Singular curves and quasi-hereditary algebras. Intern. Math. Research Notices 2017(3), 895-920 (2017) (arXiv:1503.04565 [math.AG])
  21. (with A.Plakosh) On nilpotent Chernikov p-groups with elementary tops. Arch. Math. 103 (2014) 401-409. ( arXiv:1409.7188 [math.GR]).
  22. (with V.Zembyk) Representation type of nodal algebras of type D. Ukr. Math. J. 66, No.7 (2014) 930-938.
  23. (with P.Kolesnyk) Atoms in the p-localizations of stable homotopy category. Ukr. Math. J. 66, No.4 (2014) 458-472. (arXiv:1305.2589 [math.AT])
  24. (with I.Burban and V.Gavran) Non-commutative schemes and categorical resolutions. Preprint 2014-6. Max-Plank-Institut für Mathematik, 2014.
  25. (with O.Tovpyha) Graded Cohen-Macaulay rings of wild Cohen-Macaulay type. J. Pure Appl. Algebra, 218, no.9 (2014) 1628-1634. (arXiv:1212.6557 [math.AG]).
  26. (with V.Gavran) On Cohen-Macaulay modules over non-commutative surface singularities. Cent. Eur. J. Math. 12, no.5 (2014) 675-687. (arXiv:1301.2999 [math.AG]).
  27. (with V.Zembyk) Representations of nodal algebras of type A. Algebra Discrete Math. 15, No.2 (2013), 179-200.
  28.  (with V.Bekkert and V.Futorny) Tilting, deformations and representations of linear groups over Euclidean algebras. J. Pure Appl. Algebra, 217, no.6 (2013), 1141-1152. (arXiv:0810.2037 [math.RT]) Download PDF
  29.  (with D.Voloshyn) Derived categories of nodal curves. (Ukrainian) Ukr. Math. J. 64, No.7 (2012), 1033-1040. (English translation: Ukr.Math.J. (Springer) 64 (2013), 1077-1184).
  30. (with R.Skuratovskii) One branch curve singularities with at most 2-parameter families of ideals. Algebra and Discrete Math. 13, no.2 (2012), 209-219. ( arXiv 1201.6579 [math.AC]). Download PDF
  31. (with P.Kolesnyk) On genera of polyhedra. Central European J. Math. 10 (2012), 401-410. (arXiv:1104.5526 [math.AT]). Download PDF
  32.  (with L.Bodnarchuk and G.-M.Greuel) Simple vector bundles on plane degenerations of an elliptic curve. Trans. Amer. Math. Soc.364 (2012), 137-174. ( arXiv:0903.4966 [math.AG]). Download PDF
  33. (with D.Voloshyn) Vector bundles over noncommutative nodal curves. Ukr. Math. J. 64, No.2 (2012), 185-199. (arXiv:1201.1710 [math.AG]). Download PDF
  34. (with I.Burban) Tilting on non-commutative rational projective curves. Math. Ann. 351 (2011), 665-709. (arXiv:0905.1231 [math.AG]). Download PDF
  35.  (with I.Burban) Maximal Cohen-Macaulay modules over non-isolated surface singularities. arXiv:1002.3042 [math.AG]. Download PDF
  36. (with R.Skuratovskii) Cubic rings and their ideals. Ukr. Math. J. 62,  No. 4 (2010), 530-536.   (arXiv:1001.0230 [math.AG])  Download PDF
  37. Matrix problems, triangulated categories and stable homotopy types. São Paulo Journal of Mathematical Sciences 4 (2010), 209-249. (arXiv:0903.5185 [math.AT]) Download PDF
  38. (with L.Bodnarchuk) One class of wild but brick-tame matrix problems. J.Algebra 323 (2010), 3004-3019.  ( arXiv:0903.4374 [math.RT])  Download PDF
  39. (with V.Bekkert) Derived categories for algebras with radical square zero. Algebras, Representations and Applications. Contemp. Math. 483 (2009), 55-62. ( arXiv:0812.4818 [math.RT]) Download PDF
  40. (with V.Bekkert and V.Futorny) Derived tame local and two-point algebras. J. Algebra 302 (2009), 2433-2448. (arXiv:0812.4783 [math.RT]) Download PDF
  41.  (with R.Skuratovskii) Generators and relations for wreath products. Ukrainian Math. J. 90 (2008), 997-999. (arXiv:0810.0769 [math.GR]) Download PDF
  42. (with I.Burban) Maximal Cohen-Macaulay modules over surface singularities. Trends in Representations of Algebras and Related Topics. EMS Publishing House, 2008, 101--166. (arXiv:0803.0117 [math.AG]) Download PDF
  43. Group action on bimodule categories. Algebra and Discrete Math. no. 3 (2008), 50-68. (arXiv:0802.4266 [math.RT]) Download PDF
  44. (with P.Kolesnik) Automorphisms of incidence algebras. Comm. Alg. 35 (2007). Download PDF
  45. (with V.Mazorchuk) Koszul duality for extension algebras of standard modules. J. Pure Appl. Algebra. 211 (2007), 484-496. Download PDF
  46. (with R.Bautista, Xiyangyong Zeng and Yingbo Zhang) On Hom-spaces of tame algebras. Central European J. Math. 5 (2007), 215-263. Download PDF
  47. Derived categories of modules and coherent sheaves in: Singularities and computer algebra. London Mathematical Society Lecture Note Series 324 (2006), 79-128. Download PDF
  48. (with L.Bodnarchuk, I.Burban and G.-M.Greuel) Vector bundles and torsion free sheaves on degenerations of elliptic curves. in: Global Aspects of Complex Geometry. Springer, 2006, 83-128. Download PDF
  49. (with V.M.Mazorchuk) Representation type of ${}^\infty_\lambda\mathcal H_\mu^1$. Quaterly J. Math. 57 (2006), 319--338 (arXiv:math.RT/0412301). Download PDF
  50. (with P.Kolomiets) Intersection of irreducible components of biSchubert manifolds. Zbirnyk prats’ Inst.Mat. NASU 3, №3 (2006) 180—200.
  51. (with I.Burban) Derived categories for nodal rings and projective configurations. in: Noncommutative Algebra and Geometry. Lecture Notes in Pure and Applied Mathematics 243 (2005), 23-46. Download PDF
  52. On classification of torsion free polyhedra. Preprint MPI 2005-99, Max-Plank-Institut für Mathematik, 2005. Download PDF \
  53. Semi-continuity for derived categories. Algebras and Representation Theory 8 (2005), 239--248 (arXiv:math.RT/0212015). Download PDF
  54. (with P.S.Kolomiets) On some generalization of Schubert's varieties. in: Computational commutative and non-commutative algebraic geometry. NATO Science Series III: Computer & Systems Sciences 196 (2005), 79-89.
  55. (with I.Burban) On derived categories of certain associative algebras in: Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry. Field Institute Communications 45. AMS, 2004, 109--128. Download PDF
  56. (with V.M.Mazorchuk) Koszul duality for extension algebras of standard modules. Preprint 2004-48, Uppsala University, 2004 (arXiv:math.RT/0411528). Download PDF
  57. (with E.A.Kubichka) Dimensions of finite type for representations of partially ordered sets. Algebra and Discrete Math. 3, No.3 (2004), 20-36 (arXiv:math.RT/0404242). Download PDF
  58. Matrix problems and stable homotopy types of polyhedra. Central European J. Math. 2 (2004), 420--447 (arXiv:math.AT/0404252). Download PDF
  59. (with V.I.Bekkert) Tame-wild dichotomy for derived categories. arXiv:math.RT/0310352 (submitted to J. London Math. Soc.) Download PDF
  60. Derived tame and derived wild algebras. Algebra and Discrete Math. 3, No.1 (2004), 57-74 (arXiv:math.RT/0310171). Download PDF
  61. Vector bundles and Cohen-Macaulay modules. Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry. Field Institute Communications 40. AMS, 2004, 189--222. (arXiv:math.AG/0310368) Download PDF
  62. (with L.Bodnarchuk) Stable vector bundles over cuspidal cubics. Central Eurpean J.Math. 1 (2003) 650-660. Download PDF
  63. (with I.Burban) Derived categories of nodal algebras. J. Algebra 272 (2004) 46--94. Download PDF
  64. (with G.-M. Greuel and I. Kashuba) On Cohen-Macaulay modules on surface singularities. Moscow Math. J. 3 (2003), 397-418. Download PDF
  65. On polynomial functors. Visnyk Lviv Univ., 61 (2003) 67-77. Download PDF
  66. (with I.Burban) Coherent sheaves on rational curves with simple double points and transversal intersections. Duke Math. J. 121 (2004) 189-229. Download PDF
  67. On cubic functors. Communications in Algebra, 173 (2003) 1147-1173. Download PDF
  68. (with I.Burban) Derived categories and matrix problems. In: Algebraic structures and their Applications. Ukrainian Mathematical Congress Proceedings. Institute of Mathematics, Kyiv, 2002, 201-211.
  69. Reduction algorithm and representations of boxes and algebras. Comtes Rendue Math. Acad. Sci. Canada, 23 (2001) 97-125. Download PDF
  70. (with G.-M. Greuel) Tame and wild projective curves and classification of vector bundles. J. Algebra, 246 (2001) 1-54. Download PDF
  71. (with H.-J. Baues) Classification of stable homotopy types with torsion-free homology. Topology 40 (2001) 789-821. Download PDF
  72. (with I. Burban and G.-M. Greuel) Vector bundles on singular projective curves, in: Applications of Algebraic Geometry to Coding Theory, Physics and Computation. Kluwer Academic Publishers, 2001, 1-15.
  73. Finitely generated quadratic modules, Manuscripta matem. 104 (2001), 239-256. Download PDF
  74. (with I.Burban) On derived categories of vector bundles and some associative algebras, Preprint, University of Kaiserslautern, 2001.
  75. (with H.-J. Baues) Indecomposable homotopy types with at most two non-trivial homology groups. In: Groups of Homotopy Self-Equivalences and Related Topics. Contemporary Mathematics, 274 (2001) 39-56. Download PDF
  76. Cohen-Macaulay modules and vector bundles. In: Interaction between Ring Theory and Representations of Algebras, Marcel Decker, New York, 2000, 107-130.
  77. (with H.-J. Baues) Representation theory of homotopy types with at most two non-trivial homotopy groups, Math. Proc. Cambridge Phil. Soc. 128 (2000), 283-300. Download PDF
  78. (with S. Ovsienko) Coverings of tame boxes and algebras, Preprint MPI 00-26, Max-Plank-Institut für Mathematik, Bonn, 2000 (submitted to Proceedings of the London Mathematical Society). Download PDF
  79. (with H.-J. Baues) The homotopy classification of (n-1)-connected (n+4)-dimensional polyhedra with torsion free homology, Expo. Math. 17 (1999), 161-179.Download PDF
  80. (with V. V. Kirichenko and S. A. Ovsienko) On systems of orthogonal permutations, Matem. Studii 2, no.1 (1999) 3-6.
  81. (with G.-M. Greuel) On Schappert's characterization of strictly unimodal plane curve singularities, in: Singularities: The Brieskorn Anniversary Volume, Birkhäuser, 1998, 3-26. Download PDF
  82. Module-theoretical propertiers of "good" curve singularities, in: Rings, Hopf Algebras and Brauer Groups, Marcel Decker, New York, 1998, 111-117. Download PDF
  83. Representations of bisected posets and reflection functors, In: Algebras and Modules. II, CMS Conference Proceedings, vol. 24, Amer. Math. Soc., 1998, 153-165.Download PDF
  84. (with K. W. Roggenkamp) On the global structure of regular orders of dimension two, Commun. Algebra, 25 (1997), 1-9.
  85. (with G.-M. Greuel) Semi-continuity for Cohen-Macaulay modules, Math. Ann., 306 (1996) 371-389.Download PDF
  86. (with B. L. Guzner, S. A. Ovsienko) Weight modules over generalized Weyl algebras, J. Algebra, 184 (1996) 491-504.
  87. Cohen-Macaulay modules over Cohen-Macaulay algebras. In: Representation Theory of Algebras and Related Topics, CMS Conference Proceedings, vol. 19, Amer. Math. Soc., 1996, p. 25-53. Download PDF
  88. Quadratic forms in the old Kiev school. In: Quadratic Forms in the Representation Theory of Finite-Dimensional Algebras, Bielefeld, SFB 343, 1996, 2-1 - 2-12.
  89. (with P. Dräxler, N. S. Golovashchuk, S. A. Ovsienko, M. V. Zeldich) Towards the classification of sincere weakly positive unit forms, European J. on Combinatorics, 16 (1995) 1-16.
  90. (with K. W. Roggenkamp) Cohen-Macaulay rings of global dimension two and Krull dimension two, Comm. in Algebra, 22 (1994) 3297-3330.
  91. (with V. Shapiro) Tame and wild two by two matrix orders, J. Algebra, 163 (1994) 258-264.
  92. (with V. M. Futorny, S. A. Ovsienko) Harish-Chandra subalgebras and Gelfand-Zetlin modules. In: Finite Dimensional Algebras and Related Topics, Kluwer Acad. Publ., 1994, 79-95.
  93. (with Gh. A. Noumi) Maximal orders in Lie algebra SL(2), Preprint 93-077, SFB 343, Univ. Bielefeld, 1993.
  94. (with G.-M. Greuel) Cohen-Macaulay module type, Compositio Math., 89 (1993) 315-338.Download PDF
  95. (with L. V. Izyumchenko) Representations of O-species, Ukrainian Math. J., 44 (1992) 572-574.
  96. (with G.-M. Greuel) Tame-wild dichotomy for Cohen-Macaulay modules, Math. Ann., 294 (1992) 387-394.
  97. (with V. M. Futorny, S. A. Ovsienko) Gelfand-Zetlin modules over Lie algebra SL(3), Contemp. Math., 131, p.2 (1992) 23-30.
  98. Representations of bocses and algebras, Contemp. Math. 131, p.2 (1992) 301-316.
  99. Matrix problems, small reduction and representations of a class of mixed Lie groups, In: Representations of Algebras and Related Topics, Cambridge Univ. Press, 1992, 225-249.
  100. (with S. A. Ovsienko, V. M. Futorny) On Gelfand-Zetlin modules, Suppl. Rend. Circ. Mat. Palermo, 26 (1991) 143-147.Download DjVu
  101. (with S. A. Ovsienko, V. M. Futorny) S-homomorphism of Harish-Chandra and G-modules generated by semiprimitive element, Ukrainian Math. J., 42 (1990) 1031-1037.

100.(with L. F. Chernova) On lattices over Noetherian algebras, Ukrainian Math. J., 42 (1990) 604-610.

101.(with A. S. Timoshin) Representations of net subgroups and some of their generalizations, Preprint, Kiev, 1990.

102.Finite modules over pure Noetherian algebras, Trudy Mat. Inst. Steklov Acad. Sci. USSR, 183 (1990) 56-68. (English translation: Proc. Steklov Inst. of Math., 183 (1991) 97-108) Download PDF

103.(with V. M. Futorny, S. O. Ovsienko) Irreducible weight SL(3)-modules, Funk. Anal. Prilozh., 23(3) (1989) 57-58. Download PDF

104.(with V. Chepulich) One property of an order in the free semigroup. In: Algebraic Structures and Their Applications, Kiev, 1988, 167-169.

105.(with B. Yu. Furchin, S. O. Ovsienko) Categorical constructions in representation theory, In: Algebraic Structures and Their Applications, Kiev, 1988, 17-43.

106.(with L. F. Chernova) On lattices over pseudo-Bassian commutative rings, Mat. Zametki, 41 (1987) 475-478. Download PDF

107.(with L. Kaluzhnin, S. Zavalo) Development of algebraic research at Kiev University, Visnyk Kiev Univ., 27 (1985) 52-62.

108.On existence of maximal orders, Mat. Zametki, 37 (1985) 313-315.Download PDF

109.Four squares theorem, In: Mathematics Today, Kiev, 1983, 42-49.

110.On representations of Lie algebra SL(2), Visnyk Kiev Univ., 25 (1983) 70-77.

111.Complex numbers as similitudes of plane, In the World of Math., Kiev, 12 (1981) 27-36.

112.Modules over hereditary orders, Mat. Zametki, 29 (1981) 813-816. Download PDF

113.Structure of hereditary rings, Mat. Sbornik, 113 (1980) 161-172.Download PDF

114.Tame and wild matrix problems, In: Representations and quadratic forms, Kiev, 1979, 39-74 (English translation in AMS Translations v.128).

115.(with V. M. Turchin) On locally conjugate orders, Mat. Zametki, 24 (1978) 871-878.Download PDF

116.On divisor semigroup of commutative ring, Trudy (Proc.) Steklov Math. Inst. Acad. Sci. USSR, 148 (1978) 156-167. Download PDF

117.(with V. M. Bondarenko) Representation type of finite groups, Zapiski Nauchn. Semin. LOMI, 71 (1977) 24-41. Download PDF

118.On tame and wild matrix problems, In: Matrix Problems, Kiev, 1977, 104-114.

119.Ideals of commutative rings, Mat. Sbornik, 101 (1976) 334-348.Download PDF

120.Minkowski lemma and Pell equations, In the World of Math., Kiev, 7 (1976) 32-40.

121.On generalized uniserial rings, Mat. Zametki, 18 (1975) 705-710. Download PDF

122.Pythagorean triangles and quadratic curves, In the World of Math., Kiev, 6 (1975) 26-36.

123.(with N. M. Gubareni, V. V. Kirichenko) Right serial rings, Preprint, Kiev, 1975.

124.(with A. G. Zavadski, V. V. Kirichenko) Matrix problems and integral representations, Izvestia Acad. Sci. USSR, 38 (1974) 291-293. Download PDF

125.Coxeter transformations and representations of partially ordered sets, Funk. Anal. Prilozh., 8(3) (1974) 34-42. Download PDF

126.A generalization of a theorem of Dade, Dopovidi Acad. Sci. Ukraine, 3 (1974) 204-207.

127.(with V. V. Kirichenko, K. W. Roggenkamp) Orders with one irreducible representation, Dopovidi Acad. Sci. Ukraine, 1 (1974) 22-24.

128.(with V. V. Kirichenko) Primary orders with a finite number of indecomposable representations, Izvestia Acad. Sci. USSR, 37 (1973) 715-736. Download PDF

129.Minors and theorems of reduction, Coll. Math. Soc. J.Bolyai, 6 (1973) 173-176.

130.Indecomposable matrix rings of order two with a finite number of representations are Bassian, Mat. Zametki, 12 (1972) 601-604.

131.Matrix problems and categories of matrices, Zapiski Nauchn. Semin. LOMI, 28 (1972) 144-153. Download PDF

132.Representations of commutative algebras, Funk. Anal. Prilozh., 6(4) (1972) 41-43. Download PDF

133.(with V. V. Kirichenko) On quasi-Bassian orders, Izvestia Acad. Sci. USSR, 36 (1972) 328-370. Download PDF

134.Structure of genera of representations of non-semisimple rings, Mat. Zametki, 10(1971)63-67. Download PDF

135.Ad??les and integral representations, Izvestia Acad. Sci. USSR, 33 (1969) 1080-1088. Download PDF

136.On distribution of maximal sublattices, Mat. Zametki, 6 (1969) 19-24. Download PDF

137.(with V. V. Kirichenko) Representations of totally decomposable orders, Mat. Zametki, 3 (1968) 643-650.

138.(with V. V. Kirichenko) Hereditary orders, Ukrainian Math. J., 20 (1968) 246-248.

139.(with V. V. Kirichenko, A. V. Roiter) On hereditary and Bassian orders, Izvestia Acad. Sci. USSR, 31 (1967) 1415-1436. Download PDF

140.(with V. M. Turchin) On the number of modules in a genus for integral matrix rings of order two, Mat. Zametki, 2 (1967) 133-138. Download PDF

141.(with V. V. Kirichenko) On representations of rings lying in the matrix algebra of order two, Ukrainian Math. J., 19 (1967) 107-112.

142.(with A. V. Roiter) Commutative rings with a finite number of integral indecomposable representations, Izvestia Acad. Sci. USSR, 31 (1967) 783-798. Download PDF

143.On representations of cubic Z-rings, Doklady Acad. Sci. USSR, 174 (1967) 16-18.

144.Homological algebra in semi-abelian categories, In: Algebra and Mathematical Logic, Kiev Univ., 1966, 37-43.

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