Varieties of Exponential R-Groups

IF 0.4 3区数学 Q4 LOGIC Algebra and Logic Pub Date : 2024-02-15 DOI:10.1007/s10469-024-09731-8

M. G. Amaglobeli, A. G. Myasnikov, T. T. Nadiradze

引用次数: 0

Abstract

The notion of an exponential R-group, where R is an arbitrary associative ring with unity, was introduced by R. Lyndon. Myasnikov and Remeslennikov refined the notion of an R-group by introducing an additional axiom. In particular, the new concept of an exponential MR-group (R-ring) is a direct generalization of the concept of an R-module to the case of noncommutative groups. We come up with the notions of a variety of MR-groups and of tensor completions of groups in varieties. Abelian varieties of MR-groups are described, and various definitions of nilpotency in this category are compared. It turns out that the completion of a 2-step nilpotent MR-group is 2-step nilpotent.

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指数 R 群的变种

林登（R. Lyndon）提出了指数 R 群的概念，其中 R 是具有统一性的任意关联环。米亚斯尼科夫和雷梅斯连尼科夫通过引入附加公理完善了 R 群的概念。特别是，指数 MR 群（R-环）的新概念是 R 模块概念在非交换群情况下的直接概括。我们提出了MR-群的变种和变种中群的张量补全的概念。我们描述了 MR 群的无差别群，并比较了这一范畴中的各种零势定义。事实证明，2阶零势MR群的完备性是2阶零势的。

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

Algebra and Logic 数学-数学

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions. Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. All articles are peer-reviewed.

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