Automorphisms and derivations of affine commutative and PI-algebras

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2023-11-08 DOI:10.1090/tran/9071

Oksana Bezushchak, Anatoliy Petravchuk, Efim Zelmanov

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引用次数: 0

Abstract

We prove analogs of A. Selberg’s result for finitely generated subgroups of Aut ⁡ ( A ) \operatorname {Aut}(A) and of Engel’s theorem for subalgebras of Der ⁡ ( A ) \operatorname {Der}(A) for a finitely generated associative commutative algebra A A over an associative commutative ring. We prove also an analog of the theorem of W. Burnside and I. Schur about local finiteness of torsion subgroups of Aut ⁡ ( A ) \operatorname {Aut}(A) .

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仿射交换代数和pi -代数的自同构和导数

我们证明了A. Selberg关于有限生成的Aut (A) \operatorname {Aut}(A)子群的结果和Engel关于有限生成的结合交换代数A A在结合交换环上的Der (A) \operatorname {Der}(A)子代数的定理的类似。我们还证明了W. Burnside和I. Schur关于Aut (A) \算子名{Aut}(A)的扭转子群的局部有限性的一个类似定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.