弱相容环上斜PBW扩展的单元、Gelfand和强调和环的类型

IF 0.9 Q2 MATHEMATICS

Arabian Journal of Mathematics Pub Date : 2024-12-02 DOI:10.1007/s40065-024-00485-w

Andrés Chacón, Sebastián Higuera, Armando Reyes

{"title":"弱相容环上斜PBW扩展的单元、Gelfand和强调和环的类型","authors":"Andrés Chacón, Sebastián Higuera, Armando Reyes","doi":"10.1007/s40065-024-00485-w","DOIUrl":null,"url":null,"abstract":"<div><p>We investigate and characterize several kinds of elements such as units, idempotents, von Neumann regular, <span>\\(\\pi \\)</span>-regular and clean elements for skew PBW extensions over weak compatible rings. We also study the notions of Gelfand and Harmonic rings for these families of algebras. The results presented here extend those corresponding in the literature for commutative and noncommutative rings of polynomial type.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 3","pages":"651 - 661"},"PeriodicalIF":0.9000,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-024-00485-w.pdf","citationCount":"0","resultStr":"{\"title\":\"On types of elements, Gelfand and strongly harmonic rings of skew PBW extensions over weak compatible rings\",\"authors\":\"Andrés Chacón, Sebastián Higuera, Armando Reyes\",\"doi\":\"10.1007/s40065-024-00485-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We investigate and characterize several kinds of elements such as units, idempotents, von Neumann regular, <span>\\\\(\\\\pi \\\\)</span>-regular and clean elements for skew PBW extensions over weak compatible rings. We also study the notions of Gelfand and Harmonic rings for these families of algebras. The results presented here extend those corresponding in the literature for commutative and noncommutative rings of polynomial type.</p></div>\",\"PeriodicalId\":54135,\"journal\":{\"name\":\"Arabian Journal of Mathematics\",\"volume\":\"13 3\",\"pages\":\"651 - 661\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-12-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40065-024-00485-w.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Arabian Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40065-024-00485-w\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arabian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40065-024-00485-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

研究了弱相容环上斜PBW扩展的单位元、幂等元、von Neumann正则元、\(\pi \) -正则元和清洁元等元素的性质。我们还研究了这些代数族的Gelfand和调和环的概念。本文的结果推广了文献中关于多项式型交换环和非交换环的相应结果。

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

On types of elements, Gelfand and strongly harmonic rings of skew PBW extensions over weak compatible rings

We investigate and characterize several kinds of elements such as units, idempotents, von Neumann regular, \(\pi \)-regular and clean elements for skew PBW extensions over weak compatible rings. We also study the notions of Gelfand and Harmonic rings for these families of algebras. The results presented here extend those corresponding in the literature for commutative and noncommutative rings of polynomial type.

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

Arabian Journal of Mathematics MATHEMATICS-

CiteScore

2.20

自引率

8.30%

发文量

审稿时长

13 weeks

期刊介绍： The Arabian Journal of Mathematics is a quarterly, peer-reviewed open access journal published under the SpringerOpen brand, covering all mainstream branches of pure and applied mathematics. Owned by King Fahd University of Petroleum and Minerals, AJM publishes carefully refereed research papers in all main-stream branches of pure and applied mathematics. Survey papers may be submitted for publication by invitation only.To be published in AJM, a paper should be a significant contribution to the mathematics literature, well-written, and of interest to a wide audience. All manuscripts will undergo a strict refereeing process; acceptance for publication is based on two positive reviews from experts in the field.Submission of a manuscript acknowledges that the manuscript is original and is not, in whole or in part, published or submitted for publication elsewhere. A copyright agreement is required before the publication of the paper.Manuscripts must be written in English. It is the author''s responsibility to make sure her/his manuscript is written in clear, unambiguous and grammatically correct language.