{"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><p> 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 <span>\\(G\\)</span> and\n<span>\\(G^{\\prime } \\)</span>, we prove that every special alternating semigroup\nof endomorphisms of <span>\\(G\\)</span> is isomorphic to\na suitable special alternating semigroup of endomorphisms of <span>\\(G^{\\prime } \\)</span>.\n</p>","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}
引用次数: 0
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 \(G^{\prime } \).
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
