In this paper we introduce the notion of relative syzygy modules. We then study the extension closure of the category of modules consisting of relative syzygy modules (resp. relative к-torsionfree modules).
In this paper, we first introduce the notion of generalized k-syzygy modules, and then give an equivalent characterization that the class of generalized k-syzygy modules coincides with that ofω-k-torsionfree modules....In this paper, we first introduce the notion of generalized k-syzygy modules, and then give an equivalent characterization that the class of generalized k-syzygy modules coincides with that ofω-k-torsionfree modules. We further study the extension closure of the category consisting of generalized k-syzygy modules. Some known results are obtained as corollaries.展开更多
Let A and F be left and right Noetherian rings and ∧ωr a cotilting bimodule. A necessary and sufficient condition for a finitely generated A-module to be ω-k-torsionfree is given and the extension closure of Tω^i ...Let A and F be left and right Noetherian rings and ∧ωr a cotilting bimodule. A necessary and sufficient condition for a finitely generated A-module to be ω-k-torsionfree is given and the extension closure of Tω^i is discussed. As applications, we give some results of ∧ωr related to l.id（ω） ≤ k.展开更多
基金The author was partially supported by the National Natural Science Foundation of China(Grant No.10001017)Scientifc Research Foundation for Returned Overseas Chinese Scholars(State Education Ministry) Nanjing University Talent Development Foundation.
文摘In this paper we introduce the notion of relative syzygy modules. We then study the extension closure of the category of modules consisting of relative syzygy modules (resp. relative к-torsionfree modules).
基金the Specialized Research Fund for the Doctoral Program of Higher Education (Grant Nos. 20030284033, 20060284002)the Natural Science Foundation of Jiangsu Province of China (Grant No. BK2005207)
文摘In this paper, we first introduce the notion of generalized k-syzygy modules, and then give an equivalent characterization that the class of generalized k-syzygy modules coincides with that ofω-k-torsionfree modules. We further study the extension closure of the category consisting of generalized k-syzygy modules. Some known results are obtained as corollaries.
文摘Let A and F be left and right Noetherian rings and ∧ωr a cotilting bimodule. A necessary and sufficient condition for a finitely generated A-module to be ω-k-torsionfree is given and the extension closure of Tω^i is discussed. As applications, we give some results of ∧ωr related to l.id（ω） ≤ k.
