σ-Prime Spectrum of Almost Distributive Lattices

Authors

  • Rafi Noorbhasha Bapatla Engineering College
  • Ravikumar Bandaru VIT-AP University
  • Aiyared Iampan Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand https://orcid.org/0000-0002-0475-3320

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i2.5098

Keywords:

almost distributive lattice (ADL), generalized Stone ADL, complemented ADL, relatively complemented ADL, normal ADL, minimal prime ideal, prime σ-ideal, prime α-ideal, compact space, non-dense

Abstract

For each α-ideal of an almost distributive lattice (ADL) to become a σ-ideal, a set of equivalent conditions is derived, which tends to result in a characterization of generalized Stone ADLs.  On an ADL, a one-to-one correspondence is derived between the set of all prime σ-ideals of the ADL and the set of all prime σ-ideals of the quotient ADL. Finally, proved some properties of prime σ-ideals of a normal ADL topologically.

Downloads

Published

2024-04-30

Issue

Vol. 17 No. 2: (April 2024)

Section

Nonlinear Analysis

License

Copyright (c) 2024 European Journal of Pure and Applied Mathematics

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

σ-Prime Spectrum of Almost Distributive Lattices. (2024). European Journal of Pure and Applied Mathematics, 17(2), 1094-1112. https://doi.org/10.29020/nybg.ejpam.v17i2.5098