On Ideals in Partially Ordered Ternary Semigroups

Dattatray Nabajirao Shinde, Machchhindra T. Gophane

Abstract


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.


Keywords


partially ordered ternary semigroup; bi-ideal; pseudo symmetric ideal; brouwerian lattice.

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DOI: http://dx.doi.org/10.23755/rm.v48i0.1288

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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.