恩格尔bci代数:左右对易子的应用

IF 0.3 Q4 MATHEMATICS

Mathematica Bohemica Pub Date : 2020-05-27 DOI:10.21136/mb.2020.0160-18

Ardavan Najafi, A. Saeid

{"title":"恩格尔bci代数:左右对易子的应用","authors":"Ardavan Najafi, A. Saeid","doi":"10.21136/mb.2020.0160-18","DOIUrl":null,"url":null,"abstract":". We introduce Engel elements in a BCI-algebra by using left and right normed commutators, and some properties of these elements are studied. The notion of n -Engel BCI-algebra as a natural generalization of commutative BCI-algebras is introduced, and we discuss Engel BCI-algebra, which is deﬁned by left and right normed commutators. In particular, we prove that any nilpotent BCI-algebra of type 2 is an Engel BCI-algebra, but solvable BCI-algebras are not Engel, generally. Also, it is proved that 1-Engel BCI-algebras are exactly the commutative BCI-algebras.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2020-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Engel BCI-algebras: an application of left and right commutators\",\"authors\":\"Ardavan Najafi, A. Saeid\",\"doi\":\"10.21136/mb.2020.0160-18\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We introduce Engel elements in a BCI-algebra by using left and right normed commutators, and some properties of these elements are studied. The notion of n -Engel BCI-algebra as a natural generalization of commutative BCI-algebras is introduced, and we discuss Engel BCI-algebra, which is deﬁned by left and right normed commutators. In particular, we prove that any nilpotent BCI-algebra of type 2 is an Engel BCI-algebra, but solvable BCI-algebras are not Engel, generally. Also, it is proved that 1-Engel BCI-algebras are exactly the commutative BCI-algebras.\",\"PeriodicalId\":45392,\"journal\":{\"name\":\"Mathematica Bohemica\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2020-05-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematica Bohemica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21136/mb.2020.0160-18\",\"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":"Mathematica Bohemica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21136/mb.2020.0160-18","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

利用左、右赋范交换子在BCI代数中引入Engel元素，并研究了这些元素的一些性质。引入了n-Engel BCI代数作为交换BCI代数的自然推广的概念，并讨论了由左和右赋范交换子定义的Engel BCI-代数。特别地，我们证明了任何类型2的幂零BCI代数都是Engel BCI代数，但可解BCI代数通常不是Engel。证明了1-恩格尔BCI-代数正是交换BCI-代数。

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

Engel BCI-algebras: an application of left and right commutators

. We introduce Engel elements in a BCI-algebra by using left and right normed commutators, and some properties of these elements are studied. The notion of n -Engel BCI-algebra as a natural generalization of commutative BCI-algebras is introduced, and we discuss Engel BCI-algebra, which is deﬁned by left and right normed commutators. In particular, we prove that any nilpotent BCI-algebra of type 2 is an Engel BCI-algebra, but solvable BCI-algebras are not Engel, generally. Also, it is proved that 1-Engel BCI-algebras are exactly the commutative BCI-algebras.

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

Mathematica Bohemica MATHEMATICS-

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

52 weeks