Outer inverses, minus partial orders, and triplet invariance
Journal
Publicationes Mathematicae
Journal Volume
98
Journal Issue
1-2
Pages
201-218
Date Issued
2021
Author(s)
Lin J.-H.
Abstract
In the paper, we obtain an explicit formula for the outer inverses of a regular element in an arbitrary ring. It becomes calculable for outer inverses. We characterize the triplet ba?c (resp. ba+c ) invariant under all inner inverses a? (resp. reflexive inverses a+) of a in a semiprime ring. It is also proved that if R is a regular ring and a, b, c ? R, then the triplet b?c is invariant under all outer inverses ? of a if and only if E[a] E[b] E[c] = 0. Here, for x ? R, E[x] is the smallest idempotent in the extended centroid of R such that x = E[x]x. These answer two questions in Hartwig and Patr?cio [12]. ? 2021 University of Debrecen, Institute of Mathematics. All rights reserved.
Type
journal article