Integral Classification of Endomorphisms of an Arbitrary Algebra with Finitary Operations

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2024-12-21 DOI:10.1007/s10469-024-09769-8

A. V. Litavrin

引用次数: 0

Abstract

We introduce a bipolar classification with index j for endomorphisms of an arbitrary n-groupoid with n > 1, where j = 1, 2, . . . , n. The classifications of endomorphisms constructed generalize the bipolar classification of endomorphisms of an arbitrary groupoid (i.e., a 2-groupoid) introduced previously. Using a left bipolar classification of endomorphisms of an n-groupoid (a particular case of the obtained classifications), we succeed in constructing an integral classification of endomorphisms of an arbitrary algebra (i.e., a structure without relations) with finitary operations.

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具有有限运算的任意代数自同态的积分分类

对任意n-群拟子n >的自同态引入了一个指数为j的双极分类；1，其中j = 1,2，…所构造的自同态分类推广了前面介绍的任意群似体（即2-群似体）自同态的双极性分类。利用n群拟的自同态的左双极分类（已得到分类的一个特例），我们成功地构造了具有有限运算的任意代数（即无关系结构）的自同态的积分分类。

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.