半群和环中的最小弱德拉辛倒数

IF 1.1 3区数学 Q1 MATHEMATICS

Mediterranean Journal of Mathematics 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

Mediterranean Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

261

审稿时长

6-12 weeks

期刊介绍： The Mediterranean Journal of Mathematics (MedJM) is a publication issued by the Department of Mathematics of the University of Bari. The new journal replaces the Conferenze del Seminario di Matematica dell’Università di Bari which has been in publication from 1954 until 2003. The Mediterranean Journal of Mathematics aims to publish original and high-quality peer-reviewed papers containing significant results across all fields of mathematics. The submitted papers should be of medium length (not to exceed 20 printed pages), well-written and appealing to a broad mathematical audience. In particular, the Mediterranean Journal of Mathematics intends to offer mathematicians from the Mediterranean countries a particular opportunity to circulate the results of their researches in a common journal. Through such a new cultural and scientific stimulus the journal aims to contribute to further integration amongst Mediterranean universities, though it is open to contribution from mathematicians across the world.