On Ideals in Partially Ordered Ternary Semigroups
The concept of ideals has been extensively studied through various algebraic structures such as near-rings, involution rings, regular rings, gamma-rings, semigroups, ordered semigroups, ternary semigroups and ordered ternary semigroups. In this article, we have investigated some intriguing propertie...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Accademia Piceno Aprutina dei Velati
2023-12-01
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| Series: | Ratio Mathematica |
| Subjects: | |
| Online Access: | http://eiris.it/ojs/index.php/ratiomathematica/article/view/1288 |
| Summary: | The concept of ideals has been extensively studied through various algebraic structures such as near-rings, involution rings, regular rings, gamma-rings, semigroups, ordered semigroups, ternary semigroups
and ordered ternary semigroups. In this article, we have investigated some intriguing properties of ideals, bi-ideals and pseudo symmetric ideals in partially ordered ternary semigroup T. We establish conditions for (UV W] to be an ideal, bi-ideal and pseudo symmetric ideal of T, where U, V, W are non-empty subsets of T. We prove that the family P of all pseudo symmetric ideals of T forms a Moore family of subsets of T. We also prove that the collection P of all pseudo symmetric ideals of T is a Brouwerian lattice. Also we define a pseudo
symmetric partially ordered ternary semigroup. |
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| ISSN: | 1592-7415 2282-8214 |