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EP elements in rings with involution | | Sanzhang Xu
; Jianlong Chen
; Julio Benitez
; | | Date: |
26 Feb 2016 | | Abstract: | Let $R$ be a unital ring with involution. We first show that the EP elements
in $R$ can be characterized by three equations. Namely, let $ain R$, then $a$
is EP if and only if there exists $xin R$ such that $(xa)^{ast}=xa$,
$xa^{2}=a$ and $ax^{2}=x.$ It is well known that all EP elements in $R$ are
core invertible and Moore-Penrose invertible. We give more equivalent
conditions for a core (Moore-Penrose) invertible element to be an EP element.
Finally, the EP elements are characterized in terms of $n$-EP property, which
is a generalization of bi-EP property. | | Source: | arXiv, 1602.8184 | | Services: | Forum | Review | PDF | Favorites | |
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