\((\lambda,\mu)\)-fuzzy interior ideals of ordered \(\Gamma\)-semigroups
For all \(\lambda,\mu\in [0,1]\) such that \(\lambda<\mu\), we first introduced the definitions of \((\lambda,\mu)\)-fuzzy ideals and \((\lambda,\mu)\)-fuzzy interior ideals of an ordered \(\Gamma\)-semigroup. Then we proved that in regular and in intra-regular ordered semigroups the \((\lamb...
Збережено в:
| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/755 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | For all \(\lambda,\mu\in [0,1]\) such that \(\lambda<\mu\), we first introduced the definitions of \((\lambda,\mu)\)-fuzzy ideals and \((\lambda,\mu)\)-fuzzy interior ideals of an ordered \(\Gamma\)-semigroup. Then we proved that in regular and in intra-regular ordered semigroups the \((\lambda,\mu)\)-fuzzy ideals and the \((\lambda,\mu)\)-fuzzy interior ideals coincide. Lastly, we introduced the concept of a \((\lambda,\mu)\)-fuzzy simple ordered \(\Gamma\)-semigroup and characterized the simple ordered \(\Gamma\)-semigroups in terms of \((\lambda,\mu)\)-fuzzy interior ideals. |
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