交换单元上的次直接不可还原 S 作用类的可公理化性

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2024-02-16 DOI:10.1007/s10469-024-09735-4

A. A. Stepanova, E. L. Efremov

{"title":"交换单元上的次直接不可还原 S 作用类的可公理化性","authors":"A. A. Stepanova, E. L. Efremov","doi":"10.1007/s10469-024-09735-4","DOIUrl":null,"url":null,"abstract":"An axiomatizability criterion is found for the class of subdirectly irreducible S-acts over a commutative monoid. As a corollary, a number of properties are presented which a commutative monoid should satisfy provided that the class of subdirectly irreducible acts over it is axiomatizable. The question about a complete description of monoids over which the class of subdirectly irreducible acts is axiomatizable remains open even for the case of a commutative monoid.","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Axiomatizability of the Class of Subdirectly Irreducible S-Acts over a Commutative Monoid\",\"authors\":\"A. A. Stepanova, E. L. Efremov\",\"doi\":\"10.1007/s10469-024-09735-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An axiomatizability criterion is found for the class of subdirectly irreducible S-acts over a commutative monoid. As a corollary, a number of properties are presented which a commutative monoid should satisfy provided that the class of subdirectly irreducible acts over it is axiomatizable. The question about a complete description of monoids over which the class of subdirectly irreducible acts is axiomatizable remains open even for the case of a commutative monoid.\",\"PeriodicalId\":7422,\"journal\":{\"name\":\"Algebra and Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2024-02-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra and Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10469-024-09735-4\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra and Logic","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10469-024-09735-4","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"LOGIC","Score":null,"Total":0}

引用次数: 0

摘要

为交换单元上的次直接不可还原 S 行为类找到了一个公理化标准。作为推论，我们提出了一些性质，只要交换单元上的次直接不可还原行为类是可公理化的，那么交换单元就应该满足这些性质。关于子直接不可还原行为类可公理化的单元的完整描述问题，即使对于换元单元来说，也仍然是一个悬而未决的问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Axiomatizability of the Class of Subdirectly Irreducible S-Acts over a Commutative Monoid

An axiomatizability criterion is found for the class of subdirectly irreducible S-acts over a commutative monoid. As a corollary, a number of properties are presented which a commutative monoid should satisfy provided that the class of subdirectly irreducible acts over it is axiomatizable. The question about a complete description of monoids over which the class of subdirectly irreducible acts is axiomatizable remains open even for the case of a commutative monoid.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.