Method of Verbal Operations and Automorphisms of the Category of Free Algebras

IF 0.4 3区数学 Q4 LOGIC Algebra and Logic Pub Date : 2022-10-22 DOI:10.1007/s10469-022-09679-7

E. V. Aladova

引用次数: 1

Abstract

Let an arbitrary variety of algebras and the category of all free finitely generated algebras in that variety be given. This paper is the second in a series of papers started in [Algebra and Logic, 61, No. 1, 1-15 (2022)] where we deal with automorphisms of the category of free finitely generated algebras. Here we describe in detail a method of verbal operations. The method provides a characterization of automorphisms of the category of all free finitely generated algebras in a given variety. The characterization plays a crucial role in universal algebraic geometry. We supply the reader with illuminating examples which clarify the method.

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言语运算方法与自由代数范畴的自同构

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。这篇论文是从[代数与逻辑，61，No.1，1-15（2022）]开始的一系列论文中的第二篇，在这些论文中，我们处理了自由有限生成代数范畴的自同构。在这里我们详细描述一种言语操作的方法。该方法给出了给定变种中所有自由有限生成代数范畴的自同构的一个刻画。刻画在泛代数几何中起着至关重要的作用。我们为读者提供了阐明方法的实例。

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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