부산대학교 도서관

Let A⊆Bk≥1x1,…,xn∈Na∈(N:M)={α∈A,αM⊆N}x∈Makx∈⟨x1,…,xn⟩ be two commutative rings with identity. It is well-known that if A is a Noetherian ring and B is a finitely generated A-module, then B is also a Noetherian ring. In this paper, we want to prove an analogue of the above result for SFT rings. For that, we extend the notion of SFT rings to modules. An A-module M is said to be an SFT module, if for each submodule N of M, there exist A⊆Bk≥1x1,…,xn∈Na∈(N:M)={α∈A,αM⊆N}x∈Makx∈⟨x1,…,xn⟩, A⊆Bk≥1x1,…,xn∈Na∈(N:M)={α∈A,αM⊆N}x∈Makx∈⟨x1,…,xn⟩ such that for each A⊆Bk≥1x1,…,xn∈Na∈(N:M)={α∈A,αM⊆N}x∈Makx∈⟨x1,…,xn⟩ and A⊆Bk≥1x1,…,xn∈Na∈(N:M)={α∈A,αM⊆N}x∈Makx∈⟨x1,…,xn⟩, A⊆Bk≥1x1,…,xn∈Na∈(N:M)={α∈A,αM⊆N}x∈Makx∈⟨x1,…,xn⟩. First of all, we investigate some properties of SFT modules. In fact, we show that properties of SFT rings can be generalized to SFT modules. In the end of this paper, we give a partial answer of the main question of this work.