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

Yuanfan Zhuo, Qinqin Gu and Huadong Su

Journal of Mathematics, 2024, vol. 2024, 1-10

Abstract: 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.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5289722

DOI: 10.1155/jom/5289722

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