The annihilating-submodule graph of modules over commutative rings II
نویسندگان
چکیده
منابع مشابه
ANNIHILATING SUBMODULE GRAPHS FOR MODULES OVER COMMUTATIVE RINGS
In this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. Weobserve that over a commutative ring $R$, $Bbb{AG}_*(_RM)$ isconnected 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$Bbb{A}_*(M)neq S(M)setminus {0}$, $...
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متن کاملannihilating submodule graphs for modules over commutative rings
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The rings considered in this article are commutative rings with identity $1neq 0$. The aim of this article is to define and study the exact annihilating-ideal graph of commutative rings. We discuss the interplay between the ring-theoretic properties of a ring and graph-theoretic properties of exact annihilating-ideal graph of the ring.
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ژورنال
عنوان ژورنال: Arabian Journal of Mathematics
سال: 2016
ISSN: 2193-5343,2193-5351
DOI: 10.1007/s40065-016-0154-0