π ‐Reversible ∗‐Semirings and Their Applications to Generalized Inverses

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 , a b = 0 implies there exist two positive integers m and n such that . 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, I d ‐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.