Ordered Quasi(BI)-Γ-Ideals in Ordered Γ-Semirings
In this paper, we have defined ordered quasi-Γ-ideals and ordered bi-Γ-ideals in ordered Γ-semirings by defining the relation “≤” in ordered Γ semiring S as a≤b if a+x=b for any a,b,x∈S. By using this relation we have shown that ordered quasi-Γ-ideals and ordered bi-Γ-ideals in ordered Γ-semirings a...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2019/9213536 |
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| author | Ali N. A. Koam Azeem Haider Moin A. Ansari |
| author_facet | Ali N. A. Koam Azeem Haider Moin A. Ansari |
| author_sort | Ali N. A. Koam |
| collection | DOAJ |
| description | In this paper, we have defined ordered quasi-Γ-ideals and ordered bi-Γ-ideals in ordered Γ-semirings by defining the relation “≤” in ordered Γ semiring S as a≤b if a+x=b for any a,b,x∈S. By using this relation we have shown that ordered quasi-Γ-ideals and ordered bi-Γ-ideals in ordered Γ-semirings are generalization of quasi-ideals and bi-ideals in ordered semirings. Properties of many types of ordered Γ-ideals including (semi)prime, (strongly) irreducible, and maximal ordered quasi-Γ-ideals and ordered bi-Γ-ideals in ordered Γ-semirings S have been studied. |
| format | Article |
| id | doaj-art-f6e1dbadb8e5499b8c78544b1ebc2325 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f6e1dbadb8e5499b8c78544b1ebc23252025-02-03T06:11:27ZengWileyJournal of Mathematics2314-46292314-47852019-01-01201910.1155/2019/92135369213536Ordered Quasi(BI)-Γ-Ideals in Ordered Γ-SemiringsAli N. A. Koam0Azeem Haider1Moin A. Ansari2Department of Mathematics, College of Science, Jazan University, Jazan, Saudi ArabiaDepartment of Mathematics, College of Science, Jazan University, Jazan, Saudi ArabiaDepartment of Mathematics, College of Science, Jazan University, Jazan, Saudi ArabiaIn this paper, we have defined ordered quasi-Γ-ideals and ordered bi-Γ-ideals in ordered Γ-semirings by defining the relation “≤” in ordered Γ semiring S as a≤b if a+x=b for any a,b,x∈S. By using this relation we have shown that ordered quasi-Γ-ideals and ordered bi-Γ-ideals in ordered Γ-semirings are generalization of quasi-ideals and bi-ideals in ordered semirings. Properties of many types of ordered Γ-ideals including (semi)prime, (strongly) irreducible, and maximal ordered quasi-Γ-ideals and ordered bi-Γ-ideals in ordered Γ-semirings S have been studied.http://dx.doi.org/10.1155/2019/9213536 |
| spellingShingle | Ali N. A. Koam Azeem Haider Moin A. Ansari Ordered Quasi(BI)-Γ-Ideals in Ordered Γ-Semirings Journal of Mathematics |
| title | Ordered Quasi(BI)-Γ-Ideals in Ordered Γ-Semirings |
| title_full | Ordered Quasi(BI)-Γ-Ideals in Ordered Γ-Semirings |
| title_fullStr | Ordered Quasi(BI)-Γ-Ideals in Ordered Γ-Semirings |
| title_full_unstemmed | Ordered Quasi(BI)-Γ-Ideals in Ordered Γ-Semirings |
| title_short | Ordered Quasi(BI)-Γ-Ideals in Ordered Γ-Semirings |
| title_sort | ordered quasi bi γ ideals in ordered γ semirings |
| url | http://dx.doi.org/10.1155/2019/9213536 |
| work_keys_str_mv | AT alinakoam orderedquasibigidealsinorderedgsemirings AT azeemhaider orderedquasibigidealsinorderedgsemirings AT moinaansari orderedquasibigidealsinorderedgsemirings |