Characterizations for pseudo core inverses in a ring with involution
Huihui Zhu, Pedro Henrique de Bitencourt Patricio · Linear and Multilinear Algebra · 2018
Let R be a unital ∗-ring. In this paper, we give several characterizations for the pseudo core and dual pseudo core inverses of an element by units in R. Moreover, their relations with ∗-DMP are obtained. As a special case, the existence criteria for EP elements (∗-DMP with index 1) are given. Then, the double commutant property of hybrid (b, c)-inverses is considered. Finally, the relations of the inverse along an element and the hybrid (b, c)-inverse, the (dual) pseudo core inverses and the hybrid (b, c)-inverse are investigated.