On Annihilating Graphs Associated with Modules over Commutative Rings  

作　　者：Rameez Raja Shariefuddin Pirzada 

机构地区：[1]Department of Mathematics,National Institute of Technology Srinagar Hazratbal-190006,Srinagar,India [2]Department of Mathematics,University of Kashmir Hazratbal-190006,Srinagar,India

出　　处：《Algebra Colloquium》2022年第2期281-296,共16页代数集刊（英文版）

摘　　要：Let R be a commutative ring with unity,M be a unitary R-module and F be a simple connected graph.We examine different equivalence relations on subsets A_(f)(M)\{0},A_(s)(M)\{0}and A_(t)(M)/{0}of M,where A_(f)(M)is the set of full-annihilators,A_(s)(M)is the set of semi-annihilators and A_(t)(M)is the set of star-annihilators in M.We prove that elements x,y∈M are neighborhood similar in the annihilating graph ann_(f)(Г(M))if and only if the submodules ann(x)M and ann(y)M of M are equal.We study the isomorphism of annihilating graphs arising from M and the tensor product M⊗_(R)T^(-1)R,where T=R/C(M),C(M)={r∈R|rm=O for some O≠m∈M}.

关 键 词：MODULE RING tensor product ANNIHILATOR GRAPH 

分 类 号：O15[理学—数学]