PSEUDO CORE INVERTIBILITY AND DMP INVERTIBILITY IN TWO SEMIGROUPS OF A RING WITH INVOLUTION.

In 2004, Patrício and Puystjens characterized the relation between Drazin invertible elements (resp., Moore-Penrose invertible elements) of two semigroups pRp and pRp+1 p of a ring R for some idempotent (resp., projection) p ∈ R. In this paper, we consider the relevant result for pseudo core invertible elements of such two semigroups of a ring for some projection, which is then applied to characterize the relation between pseudo core invertible elements of the matrix semigroup AA†RmxmAA†+Im AA† and the matrix semigroup A†ARnxnA†A+In A†A, where A ∈ Rmxn with A† existing. Also, similar equivalence involving DMP invertible elements is investigated. [ABSTRACT FROM AUTHOR]