A unitary right R-module MR satisfies acc on d-annihilators if for every sequence(a;);of elements of R the ascending chain AnnM(a;)■ AnnM(a;a;)■AnnM(a;a;a;)■… of submodules of MR stabilizes. In this paper ...A unitary right R-module MR satisfies acc on d-annihilators if for every sequence(a;);of elements of R the ascending chain AnnM(a;)■ AnnM(a;a;)■AnnM(a;a;a;)■… of submodules of MR stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions,the Ore extension module M[x]R[x;α,δ]over the Ore extension ring R[x;α,δ] satisfies acc on d-annihilators if and only if the module MR satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.展开更多
基金The NSF(11471108) of Chinathe NSF(2015JJ2051,2016JJ2050) of Hunan Provincethe Teaching Reform Foundation(G21316) of Hunan Province
文摘A unitary right R-module MR satisfies acc on d-annihilators if for every sequence(a;);of elements of R the ascending chain AnnM(a;)■ AnnM(a;a;)■AnnM(a;a;a;)■… of submodules of MR stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions,the Ore extension module M[x]R[x;α,δ]over the Ore extension ring R[x;α,δ] satisfies acc on d-annihilators if and only if the module MR satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.