SPECHT'S PROBLEM FOR ASSOCIATIVE AFFINE ALGEBRAS OVER COMMUTATIVE NOETHERIAN RINGS.

In a series of papers by the authors we introduced full quivers and pseudo-quivers of representations of algebras, and used them as tools in describing PI-varieties of algebras. In this paper we apply them to obtain a complete proof of Belov's solution of Specht's problem for affine algebras over an arbitrary Noetherian ring. The inductive step relies on a theorem that enables one to find a "q-characteristic coefficient-absorbing polynomial in each T-ideal I", i.e., a nonidentity of the representable algebra A arising from Γ, whose ideal of evaluations in A is closed under multiplication by q-powers of the characteristic coefficients of matrices corresponding to the generators of A, where q is a suitably large power of the order of the base field. The passage to an arbitrary Noetherian base ring C involves localizing at finitely many elements a kind of C, and reducing to the field case by a local-global principle. [ABSTRACT FROM AUTHOR]