The semisimple dimension of a certain type of module

Abstract

In this paper we define and study a new kind of dimension called, semisimple dimension, that measures how far a module is from being semisimple. Like other kinds of dimensions, this is an ordinal valued invariant. It is shown that a Noetherian module with semisimple dimension is an Artinian module. Moreover, we involve the theory of graphs within of such dimension achieving some applications for the edge ideal of a graph.