In this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. We observe that over a commutative ring $R$, $Bbb{AG}_*(_RM)$ is connected and diam$Bbb{AG}_*(_RM)leq 3$. Moreover, if $Bbb{AG}_*(_RM)$ contains a cycle, then $mbox{gr}Bbb{AG}_*(_RM)leq 4$. Also for an $R$-module $M$ with $Bbb{A}_*(M)neq S(M)setminus {0}$, $Bbb{A}_*(M)=emptyset$ if and only if $M$ is a uniform module and ann$(M)$ is a prime ideal of $R$.
Baziar, M. (2015). ANNIHILATING SUBMODULE GRAPHS FOR MODULES OVER COMMUTATIVE RINGS. Journal of Algebraic Systems, 3(1), 39-47. doi: 10.22044/jas.2015.487
MLA
M. Baziar. "ANNIHILATING SUBMODULE GRAPHS FOR MODULES OVER COMMUTATIVE RINGS". Journal of Algebraic Systems, 3, 1, 2015, 39-47. doi: 10.22044/jas.2015.487
HARVARD
Baziar, M. (2015). 'ANNIHILATING SUBMODULE GRAPHS FOR MODULES OVER COMMUTATIVE RINGS', Journal of Algebraic Systems, 3(1), pp. 39-47. doi: 10.22044/jas.2015.487
VANCOUVER
Baziar, M. ANNIHILATING SUBMODULE GRAPHS FOR MODULES OVER COMMUTATIVE RINGS. Journal of Algebraic Systems, 2015; 3(1): 39-47. doi: 10.22044/jas.2015.487
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