Some dual properties on modules

Some Properties of I-Closed Modules

Some Generalizations of Fully Dual-Stable Modules

In a previous paper we introduce the concept of full d-stability, in this work several types of generalizations were introduced ; minimal (maximal) d-stable; fully pseudo d-stable and afd-stable module. A dual to the notion of terse module is, also, introduced namely d-terse and it is shown that it is coincide with fully pseudo d-stable.

Some Properties of Generalized Local Cohomology Modules

Let R be a commutative Noetherian ring, a an ideal of R, M and N be two finitely generated R-modules. Let t be a positive integer. We prove that if R is local with maximal ideal m and M ⊗R N is of finite length then H t m (M, N) is of finite length for all t ≥ 0 and lR(H t m (M, N)) ≤ ∑t i=0 lR(Ext i R (M, H m (N))). This yields, lR(H t m (M, N)) = lR(Ext t R(M, N)). Additionally, we show that ...

T-dual Rickart modules

We introduce the notions of T-dual Rickart and strongly T-dual Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that every free (resp. finitely generated free) $R$-module is T-dual Rickart if and only if $overline{Z}^2(R)$ is a  direct summand of $R$ and End$(overline{Z}^2(R))$ is a semisimple (resp. regular) ring. It is sho...

On Some QTAG-Modules

In this paper we study totally projective QTAG-modules and the extensions of bounded QTAG-modules. In the first section we study totally projective modules M/N and M ′/N ′ where N , N ′ are isomorphic nice submodules of M and M ′ respectively. In fact the height preserving isomorphism between nice submodules is extented to the isomorphism from M onto M ′ with the help of Ulm-Kaplansky invariant...