Specht's problem for associative affine algebras over commutative Noetherian rings

Авторы: Belov-Kanel Alexei, Rowen Louis, Vishne Uzi
Журнал: ArXiv e-prints
Номер: 308.3055
Год издания: 2013
Аннотация: In a series of papers \cite{BRV1}, \cite{BRV2}, \cite{BRV3} 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 Γ," i.e., a non-identity 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.
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