On submodule spectrum in multiplication le-modules

Sachin Bhanudas  Ballal; Mayur   Kshirsagar; Sadashiv  Puranik

doi:10.13069/jacodesmath.v12i2.309

Authors

Sachin Bhanudas Ballal School of Mathematics and Statistics, University of Hyderabad, Hyderabad-500 046, India https://orcid.org/0000-0001-8757-6827
Mayur Kshirsagar Department of Mathematics, Savitribai Phule Pune University, Pune-411 007, India https://orcid.org/0009-0007-4126-5477
Sadashiv Puranik Department of Mathematics, Savitribai Phule Pune University, Pune-411 007, India

DOI:

https://doi.org/10.13069/jacodesmath.v12i2.309

Keywords:

Prime submodule element, Radical element, Zariski topology, Complete lattices, Le-modules

Abstract

In this article, we have studied the Zariski topology related to a submodule element of a le-module. Obtained a base for the complement of the submodule spectrum and topological features, along with some characterizations of the radical of a submodule element, are established. Several algebraic conditions are obtained for an open subset concerning the Zariski topology to become compact, dense, Noetherian, etc.

Received: 9 November 2023 | Accepted: 13 June 2024

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On submodule spectrum in multiplication le-modules

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