Centralizer's applications to the inverse along an element
Rings and Algebras
2016-06-14 v2
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.
Keywords
Cite
@article{arxiv.1606.02450,
title = {Centralizer's applications to the inverse along an element},
author = {Huihui Zhu and Jianlong Chen and Pedro Patricio and Xavier Mary},
journal= {arXiv preprint arXiv:1606.02450},
year = {2016}
}
Comments
14 pages