Abstract
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 “q̄-characteristic coefficient-absorbing polynomial in each T-ideal Γ”, i.e., a nonidentity of the representable algebra A arising from Γ, whose ideal of evaluations in A is closed under multiplication by q̄-powers of the characteristic coefficients of matrices corresponding to the generators of A, where q̄ 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.
Original language | English |
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Pages (from-to) | 5553-5596 |
Number of pages | 44 |
Journal | Transactions of the American Mathematical Society |
Volume | 367 |
Issue number | 8 |
DOIs | |
State | Published - 2015 |
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- General Mathematics