Inclusion properties of generalized inverses in rings
Qi Lu, Wang Long · Journal of Algebra and Its Applications · 2024
In this paper, we investigate inclusion properties in a ∗-ring. It is proven that for two [Formula: see text]-invertible elements [Formula: see text] and [Formula: see text] in a ∗-ring, [Formula: see text] if and only if [Formula: see text]. For two [Formula: see text]-invertible elements [Formula: see text] and [Formula: see text], [Formula: see text] if and only if [Formula: see text]. Moreover, we give a characterization of [Formula: see text]-inverses, and the absorption law for [Formula: see text]-inverses is studied.