∗-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, 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 giv...

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Main Authors: Yuanfan Zhuo, Qinqin Gu
Format: Article
Language:English
Published: Wiley 2024-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/jom/5289722
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author Yuanfan Zhuo
Qinqin Gu
author_facet Yuanfan Zhuo
Qinqin Gu
author_sort Yuanfan Zhuo
collection DOAJ
description 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.
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spelling doaj-art-976c240fca0d43c4b5526f875bc60d8f2025-08-20T02:36:03ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/jom/5289722∗-π-Reversible ∗-Semirings and Their Applications to Generalized InversesYuanfan Zhuo0Qinqin Gu1School of MathematicsSchool of Microelectronics & Data ScienceWe 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.http://dx.doi.org/10.1155/jom/5289722
spellingShingle Yuanfan Zhuo
Qinqin Gu
∗-π-Reversible ∗-Semirings and Their Applications to Generalized Inverses
Journal of Mathematics
title ∗-π-Reversible ∗-Semirings and Their Applications to Generalized Inverses
title_full ∗-π-Reversible ∗-Semirings and Their Applications to Generalized Inverses
title_fullStr ∗-π-Reversible ∗-Semirings and Their Applications to Generalized Inverses
title_full_unstemmed ∗-π-Reversible ∗-Semirings and Their Applications to Generalized Inverses
title_short ∗-π-Reversible ∗-Semirings and Their Applications to Generalized Inverses
title_sort ∗ π reversible ∗ semirings and their applications to generalized inverses
url http://dx.doi.org/10.1155/jom/5289722
work_keys_str_mv AT yuanfanzhuo preversiblesemiringsandtheirapplicationstogeneralizedinverses
AT qinqingu preversiblesemiringsandtheirapplicationstogeneralizedinverses