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...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}.展开更多
文摘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}.
