N. R. McConnell, R. G. McDougall, T. Stokes, L. K. Thornton
{"title":"On class operators for the lower radical class and semisimple closure constructions","authors":"N. R. McConnell, R. G. McDougall, T. Stokes, L. K. Thornton","doi":"10.1007/s10474-024-01492-1","DOIUrl":null,"url":null,"abstract":"<div><p>We construct the lower radical class and the semisimple closure\nfor a given class using class operators and detail some of the properties of these\noperators and their interplay with the operators already used in radical theory.\nThe setting is the class of algebras introduced by Puczy lowski which ensures the\nresults hold in groups, multi-operator groups such as rings, as well as loops and\nhoops.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"275 - 288"},"PeriodicalIF":0.6000,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-024-01492-1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We construct the lower radical class and the semisimple closure
for a given class using class operators and detail some of the properties of these
operators and their interplay with the operators already used in radical theory.
The setting is the class of algebras introduced by Puczy lowski which ensures the
results hold in groups, multi-operator groups such as rings, as well as loops and
hoops.
期刊介绍:
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.