PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 65(79), pp. 107--107 (1999)
On commuting generalized inverses in semigroups
Jovan D. Ke\v cki\'c and Svetozar Mili\'cFarmaceutski fakultet, Beograd, Yugoslavia and Prirodno-matemati\v cki fakultet, Novi Sad, Yugoslavia
Abstract: Let $S$ be a semigroup and let $a\in S$. In this note we describe all possible commuting generalized inverses of $a$ (in the sense of Definitions 1 and 2). It turns out that the Drazin inverse of $a$ is the only generalized inverse of $a$ which commutes with $a$.
Classification (MSC2000): 20M05
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© 2001 Mathematical Institute of the Serbian Academy of Science and Arts