Vitalij BONDARENKO
Department of Algebra,
Institute of Mathematics of NAS of Ukraine,
3 Tereshchenkivs'ka Str.,
01601 Kyiv-4, UKRAINE
E-mail: vit-bond@imath.kiev.ua

On critical quadratic forms of special type

Abstract:
We consider quadratic forms over the ring of integer number defined by (finite and infinite) posets. We call such a form critical if it is not positive but each of its proper subform is positive, and prove that a critical form is finite (i.e. defined by a finite poset).