On submodule spectrum in multiplication 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.