A characterization of ordered Γ-semigroups by ordered (m,n)-Γ-ideals
In this paper, we study (m,n)-regular ordered Γ-semigroups through ordered (m,n)-Γ-ideals. It is shown that if (S,Γ,·,≤) is an ordered Γ-semigroup; m,n are non-negative integers and A(m,n) is the set of all ordered (m,n)-Γ-ideals of S. Then, S is (m,n)-regular⇐⇒ ∀A ∈ A(m,n), A = (AmΓSΓAn]. It is al...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2020-10-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/41186 |
| _version_ | 1797633513384574976 |
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| author | Mohammad Yahya Abbasi Abul Basar Akbar Ali |
| author_facet | Mohammad Yahya Abbasi Abul Basar Akbar Ali |
| author_sort | Mohammad Yahya Abbasi |
| collection | DOAJ |
| description |
In this paper, we study (m,n)-regular ordered Γ-semigroups through ordered (m,n)-Γ-ideals. It is shown that if (S,Γ,·,≤) is an ordered Γ-semigroup; m,n are non-negative integers and A(m,n) is the set of all ordered (m,n)-Γ-ideals of S. Then, S is (m,n)-regular⇐⇒ ∀A ∈ A(m,n), A = (AmΓSΓAn]. It is also proved that if (S,Γ,·,≤) is an ordered Γ-semigroup and m,n are nonnegative integers and R(m,0) and L(0,n) is the set of all (m,0)-Γideals and (0,n)-Γ-ideals of S, respectively. Then, S is (m,n)-regular ordered Γ semigroup ⇐⇒∀R ∈R(m,0)∀L ∈L(0,n),R∩L = (RmΓL∩RΓLn].
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| first_indexed | 2024-03-11T11:55:04Z |
| format | Article |
| id | doaj.art-b50319ec5e414431b70665edaef49a25 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-03-11T11:55:04Z |
| publishDate | 2020-10-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-b50319ec5e414431b70665edaef49a252023-11-08T20:01:09ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882020-10-0139410.5269/bspm.41186A characterization of ordered Γ-semigroups by ordered (m,n)-Γ-idealsMohammad Yahya Abbasi0Abul Basar1Akbar Ali2Jamia Millia IslamiaJamia Millia IslamiaJamia Millia Islamia In this paper, we study (m,n)-regular ordered Γ-semigroups through ordered (m,n)-Γ-ideals. It is shown that if (S,Γ,·,≤) is an ordered Γ-semigroup; m,n are non-negative integers and A(m,n) is the set of all ordered (m,n)-Γ-ideals of S. Then, S is (m,n)-regular⇐⇒ ∀A ∈ A(m,n), A = (AmΓSΓAn]. It is also proved that if (S,Γ,·,≤) is an ordered Γ-semigroup and m,n are nonnegative integers and R(m,0) and L(0,n) is the set of all (m,0)-Γideals and (0,n)-Γ-ideals of S, respectively. Then, S is (m,n)-regular ordered Γ semigroup ⇐⇒∀R ∈R(m,0)∀L ∈L(0,n),R∩L = (RmΓL∩RΓLn]. https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/41186 |
| spellingShingle | Mohammad Yahya Abbasi Abul Basar Akbar Ali A characterization of ordered Γ-semigroups by ordered (m,n)-Γ-ideals Boletim da Sociedade Paranaense de Matemática |
| title | A characterization of ordered Γ-semigroups by ordered (m,n)-Γ-ideals |
| title_full | A characterization of ordered Γ-semigroups by ordered (m,n)-Γ-ideals |
| title_fullStr | A characterization of ordered Γ-semigroups by ordered (m,n)-Γ-ideals |
| title_full_unstemmed | A characterization of ordered Γ-semigroups by ordered (m,n)-Γ-ideals |
| title_short | A characterization of ordered Γ-semigroups by ordered (m,n)-Γ-ideals |
| title_sort | characterization of ordered γ semigroups by ordered m n γ ideals |
| url | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/41186 |
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