论一个类群的内变形的交替半群

Siberian Advances in Mathematics Pub Date : 2024-05-31 DOI:10.1134/s1055134424020032

A. V. Litavrin

{"title":"论一个类群的内变形的交替半群","authors":"A. V. Litavrin","doi":"10.1134/s1055134424020032","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3> We study the bipolar type of the composition for pairs of endomorphisms of a groupoid\nand introduce the notion of an alternating pair of endomorphisms. For such a pair, the bipolar\ntype of the composition is represented in terms of the bipolar types of the initial endomorphisms.\nWe suggest an explicit formula for this representation. We also introduce alternating and special\nalternating semigroups of endomorphisms of a groupoid so that every pair of endomorphisms from\nan alternating semigroup is alternating. For every groupoid, we prove that the base set of\nendomorphisms of the first type is a special alternating semigroup with identity (i.e., a monoid).\nFor isomorphic groupoids \\(G\\) and\n\\(G^{\\prime } \\), we prove that every special alternating semigroup\nof endomorphisms of \\(G\\) is isomorphic to\na suitable special alternating semigroup of endomorphisms of \\(G^{\\prime } \\).\n","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"52 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Alternating Semigroups of Endomorphisms of a Groupoid\",\"authors\":\"A. V. Litavrin\",\"doi\":\"10.1134/s1055134424020032\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3> We study the bipolar type of the composition for pairs of endomorphisms of a groupoid\\nand introduce the notion of an alternating pair of endomorphisms. For such a pair, the bipolar\\ntype of the composition is represented in terms of the bipolar types of the initial endomorphisms.\\nWe suggest an explicit formula for this representation. We also introduce alternating and special\\nalternating semigroups of endomorphisms of a groupoid so that every pair of endomorphisms from\\nan alternating semigroup is alternating. For every groupoid, we prove that the base set of\\nendomorphisms of the first type is a special alternating semigroup with identity (i.e., a monoid).\\nFor isomorphic groupoids \\\\(G\\\\) and\\n\\\\(G^{\\\\prime } \\\\), we prove that every special alternating semigroup\\nof endomorphisms of \\\\(G\\\\) is isomorphic to\\na suitable special alternating semigroup of endomorphisms of \\\\(G^{\\\\prime } \\\\).\\n\",\"PeriodicalId\":39997,\"journal\":{\"name\":\"Siberian Advances in Mathematics\",\"volume\":\"52 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Siberian Advances in Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1134/s1055134424020032\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Advances in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1055134424020032","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

摘要我们研究了类群的成对内定态的组合的双极性类型，并引入了交替成对内定态的概念。对于这样的一对，组合的双极性类型用初始内定形的双极性类型来表示。我们还引入了类群内同态的交替半群和特殊交替半群，这样交替半群的每一对内同态都是交替的。对于每一个类群，我们都证明了第一类内同构的基集是一个具有同一性的特殊交替半群（即一个单元）。对于同构的类群 \(G\) 和 \(G^{\prime } \)，我们证明了 \(G\) 的每一个特殊交替内同构半群都与\(G^{/prime } \)的一个合适的特殊交替内同构半群同构。

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

On Alternating Semigroups of Endomorphisms of a Groupoid

Abstract

We study the bipolar type of the composition for pairs of endomorphisms of a groupoid and introduce the notion of an alternating pair of endomorphisms. For such a pair, the bipolar type of the composition is represented in terms of the bipolar types of the initial endomorphisms. We suggest an explicit formula for this representation. We also introduce alternating and special alternating semigroups of endomorphisms of a groupoid so that every pair of endomorphisms from an alternating semigroup is alternating. For every groupoid, we prove that the base set of endomorphisms of the first type is a special alternating semigroup with identity (i.e., a monoid). For isomorphic groupoids \(G\) and \(G^{\prime } \), we prove that every special alternating semigroup of endomorphisms of \(G\) is isomorphic to a suitable special alternating semigroup of endomorphisms of \(G^{\prime } \).

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

Siberian Advances in Mathematics Mathematics-Mathematics (all)

CiteScore

0.70

自引率

0.00%

发文量

期刊介绍： Siberian Advances in Mathematics is a journal that publishes articles on fundamental and applied mathematics. It covers a broad spectrum of subjects: algebra and logic, real and complex analysis, functional analysis, differential equations, mathematical physics, geometry and topology, probability and mathematical statistics, mathematical cybernetics, mathematical economics, mathematical problems of geophysics and tomography, numerical methods, and optimization theory.