(b, c)-逆的逆序律和正序律

IF 0.7 4区 数学 Q2 Mathematics
Jelena Višnjić, Ivana Stanisev, Y. Ke
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引用次数: 0

摘要

研究了各种类型广义逆的逆序律和正序律。$(b,c)$-逆是一些众所周知的广义逆的推广,如Moore-Penrose逆、Drazin逆、core逆等。本文研究了一元环上$(b,c)$-逆的逆序律,并导出了该律对$(b,c)$逆成立的等价条件。此外,对这一主题的一些已知结果进行了推广。进一步,给出了具有单位环中$(b,c)$-逆在$b$和$c$的不同选择下的正序律。此外,作为所得结果的推论,导出了逆阶律和逆阶律沿单元正序律的等价条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Reverse order law and forward order law for the (b, c)-inverse
The reverse order law and the forward order law have been studied for various types of generalized inverses. The $(b,c)$-inverse is a generalization of some well known generalized inverses, such as the Moore-Penrose inverse, the Drazin inverse, the core inverse, etc. In this paper, the reverse order law for the $(b,c)$-inverse, in a unital ring, is investigated and an equivalent condition for this law to hold for the $(b,c)$-inverse is derived. Also, some known results on this topic are generalized. Furthermore, the forward order law for the $(b,c)$-inverse in a ring with a unity is introduced, for different choices of $b$ and $c$. Moreover, as corollaries of obtained results, equivalent conditions for the reverse order law and the forward order law for the inverse along an element are derived.
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来源期刊
CiteScore
1.20
自引率
14.30%
发文量
45
审稿时长
6-12 weeks
期刊介绍: The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.
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