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).