Centralizer’s applications to the inverse along an element

Huihui Zhu, Jianlong Chen, Pedro Patrício and Xavier Mary

Applied Mathematics and Computation, 2017, vol. 315, issue C, 27-33

Abstract: In this paper, we firstly prove that the absorption law for one-sided inverses along an element holds, and derive the absorption law for the inverse along an element. We then obtain the absorption law for the inverse along different elements. Also, we prove that a left inverse of a along d coincides with a right inverse of a along d, provided that they both exist. Then, the reverse order law and the existence criterion for the inverse along an element are given by centralizers in a ring. Finally, we characterize the Moore–Penrose inverse of a regular element by one-sided invertibilities in a ring with involution.

Keywords: Absorption laws; Reverse order laws; Centralizers; Left (Right) inverses along an element; Inverses along an element; Moore–Penrose inverses (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:315:y:2017:i:c:p:27-33

DOI: 10.1016/j.amc.2017.07.046

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