{"docId":10273,"paperId":10273,"url":"https:\/\/cm.episciences.org\/10273","doi":"10.46298\/cm.10273","journalName":"Communications in Mathematics","issn":"1804-1388","eissn":"2336-1298","volume":[{"vid":673,"name":"Volume 31 (2023), Issue 1"}],"section":[],"repositoryName":"arXiv","repositoryIdentifier":"2211.03235","repositoryVersion":2,"repositoryLink":"https:\/\/arxiv.org\/abs\/2211.03235v2","dateSubmitted":"2022-11-08 10:30:08","dateAccepted":"2022-11-08 19:18:45","datePublished":"2022-11-11 10:28:37","titles":["On Strongly pi-Regular Rings with Involution"],"authors":["Cui, Jian","Danchev, Peter"],"abstracts":["Recall that a ring R is called strongly pi-regular if, for every a in R, there is a positive integer n, depending on a, such that a^n belongs to the intersection of a^{n+1}R and Ra^{n+1}. In this paper we give a further study of the notion of a strongly pi-star-regular ring, which is the star-version of strongly pi-regular rings and which was originally introduced by Cui-Wang in J. Korean Math. Soc. (2015). We also establish various properties of these rings and give several new characterizations in terms of (strong) pi-regularity and involution. Our results also considerably extend recent ones in the subject due to Cui-Yin in Algebra Colloq. (2018) proved for pi-star-regular rings and due to Cui-Danchev in J. Algebra Appl. (2020) proved for star-periodic rings.","Comment: 8 pages"],"keywords":["Mathematics - Rings and Algebras","16E50, 16W10"]}