On submodule spectrum in multiplication le-modules

Sachin Bhanudas  Ballal; Mayur   Kshirsagar; Sadashiv  Puranik

Sachin Bhanudas Ballal
Mayur Kshirsagar Savitribai Phule Pune University, Pune-411 007 (INDIA)
Sadashiv Puranik

Keywords: Prime submodule element, radical element, Zariski topology, complete lattices; le-modules etc.

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.