Uniqueness of primary decompositions in Laskerian 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 $(M,+,⩽,e)$ 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.

17 pages