ANNIHILATING SUBMODULE GRAPHS FOR MODULES OVER COMMUTATIVE RINGS

In this article, we give several generalizations of the concept of annihilating an ideal graph over a commutative ring with identity to modules. We observe that, over a commutative ring, R, AG(RM) is connected, and diamAG(RM) ? 3. More- over, if AG(RM) contains a cycle, then grAG(RM) ? 4. Also for an R-module M with A(M) ?= S(M) \ {0}, A(M) = ?, if and only if M is a uniform module, and ann(M) is a prime ideal of R.