交换弱调用-清洁群环

Q3 Mathematics

Ural Mathematical Journal Pub Date : 2019-07-25 DOI:10.15826/UMJ.2019.1.005

P. Danchev

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引用次数: 0

摘要

一个环\(R\)如果它的任何元素是对合和幂等的和或差，则称为弱对合环。对于每一个交换一元环\(R\)和每一个阿贝尔群\(G\)，我们只在\(R\), \(G\)及其节的项中找到了群环\(R[G]\)弱邀约的充分必要条件。我们建立的结果与danchevv - mcgovern在J. Algebra(2015)上发表的结果相似，并证明了弱零清洁环。

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Commutative Weakly Invo–Clean Group Rings

A ring \(R\) is called weakly invo-clean if any its element is the sum or the difference of an involution and an idempotent. For each commutative unital ring \(R\) and each abelian group \(G\), we find only in terms of \(R\), \(G\) and their sections a necessary and sufficient condition when the group ring \(R[G]\) is weakly invo-clean. Our established result parallels to that due to Danchev-McGovern published in J. Algebra (2015) and proved for weakly nil-clean rings.

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来源期刊

Ural Mathematical Journal Mathematics-Mathematics (all)

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

16 weeks