{"title":"n-fine环","authors":"Nabil Zeidi","doi":"10.18514/mmn.2023.3724","DOIUrl":null,"url":null,"abstract":". A ring R is said to be n -fine if every nonzero element in R can be written as a sum of a nilpotent and n units in R. The class of these rings contains fine rings and n -good rings in which each element is a sum of n units. Fundamental properties of such rings are obtained. One of the main results of this paper is that the m × m matrix ring M m ( R ) over any arbitrary ring R is 2-fine. Furthermore, the m × m matrix ring M m ( R ) over a n -fine ring R is n -fine.","PeriodicalId":49806,"journal":{"name":"Miskolc Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"n-fine rings\",\"authors\":\"Nabil Zeidi\",\"doi\":\"10.18514/mmn.2023.3724\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". A ring R is said to be n -fine if every nonzero element in R can be written as a sum of a nilpotent and n units in R. The class of these rings contains fine rings and n -good rings in which each element is a sum of n units. Fundamental properties of such rings are obtained. One of the main results of this paper is that the m × m matrix ring M m ( R ) over any arbitrary ring R is 2-fine. Furthermore, the m × m matrix ring M m ( R ) over a n -fine ring R is n -fine.\",\"PeriodicalId\":49806,\"journal\":{\"name\":\"Miskolc Mathematical Notes\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Miskolc Mathematical Notes\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.18514/mmn.2023.3724\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Miskolc Mathematical Notes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.18514/mmn.2023.3724","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
摘要
． 是说to be A环R n -fine,如果每nonzero元素在R可以成为美国就读(sum of A nilpotent and n单位在R级》。这些戒指containsfine每响与n -响》,这是元素A sum of n单位。《指环》的基本性质受到质疑。玩results》这篇文章的一个那是mm×m矩阵环(R)通过任何arbitrary环R是2 -fine)。Furthermore,《mm×m矩阵环(R)通过a n -fi东北环R是n -fine。
. A ring R is said to be n -fine if every nonzero element in R can be written as a sum of a nilpotent and n units in R. The class of these rings contains fine rings and n -good rings in which each element is a sum of n units. Fundamental properties of such rings are obtained. One of the main results of this paper is that the m × m matrix ring M m ( R ) over any arbitrary ring R is 2-fine. Furthermore, the m × m matrix ring M m ( R ) over a n -fine ring R is n -fine.
期刊介绍：
Miskolc Mathematical Notes, HU ISSN 1787-2405 (printed version), HU ISSN 1787-2413 (electronic version), is a peer-reviewed international mathematical journal aiming at the dissemination of results in many fields of pure and applied mathematics.
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