ON AN $\omega$-EDGE IDEAL OF A SIMPLE GRAPH

Abstract

Considering a commutative ring $R$ with non-zero identity and the $R$-module $I(G)$, which is the edge ideal of a finite simple graph $G$, with no isolated vertex, we introduce the notion of an $\omega$-edge ideal, which is a module. We establish some results which involve the sum of $\omega$-edge ideals.