Automorphisms of the Category of Free Finitely Generated Algebras

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2022-08-06 DOI:10.1007/s10469-022-09671-1

E. V. Aladova

引用次数: 3

Abstract

Let an arbitrary variety of algebras and the category of all free finitely generated algebras in that variety be given. In universal algebraic geometry over an arbitrary variety of algebras, the group of automorphisms of the category of free finitely generated algebras plays an important role. This paper is first in a series where we will deal with the group mentioned. Here we describe properties of automorphisms of the category of all free finitely generated algebras and distinguish two important subgroups: namely, the subgroup of inner automorphisms and the subgroup of strongly stable automorphisms.

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自由有限生成代数范畴的自同构

给定任意一个代数的变种和该变种中所有自由有限生成代数的范畴。在任意代数上的泛代数几何中，自由有限生成代数范畴的自同构群起着重要作用。这篇论文是我们将讨论上述小组的系列文章中的第一篇。在这里，我们描述了所有自由有限生成代数范畴的自同构的性质，并区分了两个重要的子群：即内自同构的子群和强稳定自同构的子集。

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.