Uniqueness of primary decompositions in Laskerian le-modules

TL;DR

This paper introduces a new class of lattice-ordered modules over rings, establishing theorems on the uniqueness of primary decompositions within this framework.

Contribution

It defines and characterizes a novel class of le-modules and proves uniqueness theorems for primary decompositions in these modules.

Findings

Defined and characterized a new class of le-modules.

Proved theorems on the uniqueness of primary decompositions.

Established foundational notions for primary decomposition in le-modules.

Abstract

Here we introduce and characterize a new class of le-modules $_{R}M$ where $R$ is a commutative ring with $1$ and $(M,+,\leqslant,e)$ is a lattice ordered semigroup with the greatest element $e$. Several notions are defined and uniqueness theorems for primary decompositions of a submodule element in a Laskerian le-module are established.