半群和环中的最小弱德拉辛倒数

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-13 DOI:10.1007/s00009-024-02661-w

Shuxian Xu, Jianlong Chen, Cang Wu

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引用次数: 0

摘要

1978 年，坎贝尔和迈耶提出了复数矩阵的最小秩弱 Drazin 逆的概念。在本文中，我们使用格林前序（Green's preorder \(\leqslant_{\mathcal{R}}},\)）定义了半群中元素的最小弱 Drazin 逆，它概括了复矩阵的最小秩弱 Drazin 逆。对于半群的两个元素 a, y，证明了 y 是 a 的最小弱 Drazin 逆，当且仅当 \(ya^{k+1}=a^{k}\) 对于某个非负整数 k 并且 \(ay^{2}=y.\) 时。

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Minimal Weak Drazin Inverses in Semigroups and Rings

In 1978, Campbell and Meyer proposed the notion of minimal rank weak Drazin inverses of complex matrices. In this paper, we define minimal weak Drazin inverses of elements in semigroups using Green’s preorder \(\leqslant _{{\mathcal {R}}},\) which generalize minimal rank weak Drazin inverses of complex matrices. For two elements a, y of a semigroup, it is proved that y is a minimal weak Drazin inverse of a if and only if \(ya^{k+1}=a^{k}\) for some nonnegative integer k and \(ay^{2}=y.\)

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.