ИСТИНА

Let A be an algebra with generators a_1,...,a_s and relations f_1,...,f_r. We are interested in the highest terms in the ideal of relations. If U is a highest term and S and T are words, then SUT is a highest term as well, which we call a trivial corollary of U. We are interested in the highest terms which are not trivial corollaries. The cogrowth function of the algebra A is the number V(n) of nontrivial highest terms of length n. We prove that the cogrowth function of a finitely presented algebra is either asymptotically constant (in this case a Groebner basis of relations is finite) or no less than logarithmic in n. We investigate cogrowth functions of different classes of algebras and different classes of words.