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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2019-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2019/9213536 |
| Summary: | 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. |
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| ISSN: | 2314-4629 2314-4785 |