On Ideals in Partially Ordered Ternary Semigroups

Authors

  • Dattatray Nabajirao Shinde Shivaji University, Kolhapur-416004, Maharashtra, India
  • Machchhindra T. Gophane Shivaji University, Kolhapur-416004, Maharashtra, India

DOI:

https://doi.org/10.23755/rm.v48i0.1288

Keywords:

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

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.

References

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Published

2023-12-30

Issue

Vol. 48 (2023)

Section

Volume 48-2023

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