Year: 2024
Type: article
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 . 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.
Source: Journal of Mathematics
DOI: 10.1155/jom/5289722
Authors: Yuanfan Zhuo, Qinqin Gu
Institutions: Northwest University, Anhui University of Technology
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,060
OpenAlex ID: W4404763263