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arXiv · 1606.02450

Centralizer's applications to the inverse along an element

Huihui Zhu·Jianlong Chen·Pedro Patricio·Xavier Mary
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Abstract

In this paper, we first prove that the absorption law for one-sided inverses along an element holds, deriving the absorption law for the inverse along an element. We then apply this result to obtain the absorption law for the inverse along different elements. Also, 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 by one-sided invertibilities in a ring with involution.

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Huihui Zhu, Jianlong Chen, Pedro Patricio, Xavier Mary. 2016-06-08. Centralizer's applications to the inverse along an element. https://arxiv.org/abs/1606.02450

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