∗-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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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/jom/5289722 |
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| _version_ | 1850117579120574464 |
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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. |
| format | Article |
| id | doaj-art-976c240fca0d43c4b5526f875bc60d8f |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| 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 |