∗-π-Reversible ∗-Semirings and Their Applications to Generalized Inverses - Yuanfan Zhuo; Qinqin Gu (Journal of Mathematics)
We introduce and study a new class of ∗-semirings which is called ∗-π-reversible ∗-semirings. A ∗-semiring R is said to be ∗-π-reversible if for any a,b∈R, ab=0 implies there exist two positive integers m and n such that bman∗=0. Some characterizations and examples of this class of semirings are given. As applications, generalized inverses related to ∗-π-reversible ∗-semirings are studied. For an additive cancellative, Id-complemented and ∗-π-reversible ∗-semiring R, if a∈R is reflexive invertible, some equivalent characterizations of a being normal elements and strong EP elements are given.