n-fine环

IF 0.9 4区数学 Q1 Mathematics

Miskolc Mathematical Notes Pub Date : 2023-01-01 DOI:10.18514/mmn.2023.3724

Nabil Zeidi

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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。

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n-fine rings

. 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.

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来源期刊

Miskolc Mathematical Notes Mathematics-Algebra and Number Theory

CiteScore

2.00

自引率

0.00%

发文量

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.