The Kurosh problem, height theorem, nilpotency of the radical, and algebraicity identity

Автор: Belov A.Ya
Журнал: Journal of Math. science NY
Том: 154
Номер: 2
Год издания: 2008
Первая страница: 125
Последняя страница: 142
DOI: 10.1007/s10958-008-9156-6
Аннотация: This paper is devoted to relations between the Kurosh problem and the Shirshov height theorem. The central point and main technical tool is the identity of algebraicity. The main result is as follows. Let $A$ be a finitely generated PI-algebra and $Y$ be a finite subset of $A$. Suppose that for any Noetherian associative and commutative ring $R\supset\bbfF$, any factor of $R\otimes A$ such that all projections of elements from $Y$ are algebraic over $\pi(R)$ is a Noetherian $R$-module. Then $A$ has bounded essential height over $Y$. If, furthermore, $Y$ generates $A$ as an algebra, then $A$ has bounded height over $Y$ in Shirshov's sense. This paper also contains a new proof of the Razmyslov-Kemer-Braun theorem on nilpotence of the radical for an affine PI-algebra. The proof allows to obtain constructive estimates.Reviewer: Victor Petrogradsky (Ulyanovsk)
Добавил в систему: Белов Алексей Яковлевич

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