{"title":"$ E $ -环与商可除阿贝尔群","authors":"M. N. Zonov, E. A. Timoshenko","doi":"10.1134/s003744662306006x","DOIUrl":null,"url":null,"abstract":"<p>Under study are the relations between <span>\\( E \\)</span>-rings and quotient divisible abelian groups.\nWe obtain a criterion for the quotient divisibility of the additive group\nof an <span>\\( E \\)</span>-ring and give a negative solution to the Bowshell and Schultz problem\nabout the quasidecompositions of <span>\\( E \\)</span>-rings.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"$ E $ -Rings and Quotient Divisible Abelian Groups\",\"authors\":\"M. N. Zonov, E. A. Timoshenko\",\"doi\":\"10.1134/s003744662306006x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Under study are the relations between <span>\\\\( E \\\\)</span>-rings and quotient divisible abelian groups.\\nWe obtain a criterion for the quotient divisibility of the additive group\\nof an <span>\\\\( E \\\\)</span>-ring and give a negative solution to the Bowshell and Schultz problem\\nabout the quasidecompositions of <span>\\\\( E \\\\)</span>-rings.</p>\",\"PeriodicalId\":49533,\"journal\":{\"name\":\"Siberian Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-11-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Siberian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s003744662306006x\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s003744662306006x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
研究了\( E \) -环与商可除的阿贝尔群之间的关系。得到了\( E \) -环加性群商可除性的一个判据，并给出了\( E \) -环拟复合的Bowshell和Schultz问题的一个负解。
$ E $ -Rings and Quotient Divisible Abelian Groups
Under study are the relations between \( E \)-rings and quotient divisible abelian groups.
We obtain a criterion for the quotient divisibility of the additive group
of an \( E \)-ring and give a negative solution to the Bowshell and Schultz problem
about the quasidecompositions of \( E \)-rings.
期刊介绍：
Siberian Mathematical Journal is journal published in collaboration with the Sobolev Institute of Mathematics in Novosibirsk. The journal publishes the results of studies in various branches of mathematics.
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