斜单弦环上的强清洁矩阵环

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2023-08-29 DOI:10.1142/s1005386723000305

Arezou Karimimansoub, Mohammad-Reza (Rafsanjani) Sadeghi

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引用次数: 0

摘要

设[公式:见文]是一个具有自同态的环[公式:见文]，[公式:见文]是由[公式:见文]生成的加了0的自由单群，[公式:见文]是将[公式:见文]中的某些单项式设为0而得到的[公式:见文]因子，使得[公式:见文]对某些[公式:见文]而言是[公式:见文]。然后我们就可以形成非半素数偏斜的单弦环[公式:见文]。如果对于任意[公式:见文]和任意[公式:见文]，[公式:见文]的阿贝尔群自同态[公式:见文]和[公式:见文]是满射，则局部环[公式:见文]被称为漂白。使用[公式:见正文]，我们提供各种类型的漂白和未漂白局部环。关于强清洁环的主要问题之一是表征矩阵环[公式:见文本]是强清洁的环[公式:见文本]。我们研究了满矩阵环在偏单峰环上的强清洁性[公式:见原文]。

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Strongly Clean Matrix Rings over a Skew Monoid Ring

Let [Formula: see text] be a ring with an endomorphism [Formula: see text], [Formula: see text] the free monoid generated by [Formula: see text] with 0 added, and [Formula: see text] a factor of [Formula: see text] obtained by setting certain monomials in [Formula: see text] to 0 such that [Formula: see text] for some [Formula: see text]. Then we can form the non-semiprime skew monoid ring [Formula: see text]. A local ring [Formula: see text] is called bleached if for any [Formula: see text] and any [Formula: see text], the abelian group endomorphisms [Formula: see text] and [Formula: see text] of [Formula: see text] are surjective. Using [Formula: see text], we provide various classes of both bleached and non-bleached local rings. One of the main problems concerning strongly clean rings is to characterize the rings [Formula: see text] for which the matrix ring [Formula: see text] is strongly clean. We investigate the strong cleanness of the full matrix rings over the skew monoid ring [Formula: see text].

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来源期刊

Algebra Colloquium 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

625

审稿时长

15.6 months

期刊介绍： Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.