Representability of relatively free affine algebras over a Noetherian ring

Авторы: Kanel-Belov Alexei, Rowen Louis, Vishne Uzi
Журнал: ArXiv e-prints
Номер: 2209.01494
Год издания: 2022
DOI: 10.48550/ARXIV.2209.01494
Аннотация: Kemer proved in 1988 that every affine relatively free PI algebra over an infinite field, is representable. In 2010, the first author of this paper proved more generally that every affine relatively free PI algebra over any commutative Noetherian unital ring is representable. In this paper we present a different, complete, proof, based on new techniques: the notion of a full quiver of algebras, and "hiking," developed in our previous treatment of Specht's problem in the affine case in the Transactions of the AMS.The bulk of the proof is for the case of a base field of positive characteristic. Here, whereas the usage of hiking is more direct, one must consider nonhomogeneous polynomials when the base ring is finite, which creates certain difficulties to be overcome. We conclude with a Noetherian induction on T-ideals.
Добавил в систему: Белов Алексей Яковлевич

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