{"title":"关于一些幂零大括号的结构","authors":"M. Dixon, L. A. Kurdachenko","doi":"10.15421/242303","DOIUrl":null,"url":null,"abstract":"We prove a criteria for nilpotency of left braces in terms of the $\\star$-central series and also discuss Noetherian braces, obtaining some of their elementary properties. We also show that if a finitely generated brace $A$ is Smoktunowicz-nilpotent, then the additive and multiplicative groups of $A$ are likewise finitely generated.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":"19 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the structure of some nilpotent braces\",\"authors\":\"M. Dixon, L. A. Kurdachenko\",\"doi\":\"10.15421/242303\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove a criteria for nilpotency of left braces in terms of the $\\\\star$-central series and also discuss Noetherian braces, obtaining some of their elementary properties. We also show that if a finitely generated brace $A$ is Smoktunowicz-nilpotent, then the additive and multiplicative groups of $A$ are likewise finitely generated.\",\"PeriodicalId\":52827,\"journal\":{\"name\":\"Researches in Mathematics\",\"volume\":\"19 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Researches in Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15421/242303\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Researches in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15421/242303","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
摘要
我们证明了左括号在$\ * $-中心级数上幂零的一个判据，并讨论了Noetherian括号，得到了它们的一些基本性质。我们也证明了如果一个有限生成的括号$ a $是smoktunowicz -幂零的，那么$ a $的加性和乘性群同样是有限生成的。
We prove a criteria for nilpotency of left braces in terms of the $\star$-central series and also discuss Noetherian braces, obtaining some of their elementary properties. We also show that if a finitely generated brace $A$ is Smoktunowicz-nilpotent, then the additive and multiplicative groups of $A$ are likewise finitely generated.
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
