In this paper we will first establish a duality between in jectivity and flatness for modules.
That is: Let E be a faithfully in jective module". Then, for each module A, we have W, dim. A …

Let R be a commutative ring with a unit element. If there exist no proper ideals a, such that
R= a (+) b, then R is said to be indecomposable. If the number of maximal ideals of R is …

Suppose (R, m) and (S, n) are commutative Noetherian local rings and ϕ: R→ S is a flat
local homomorphism with the property that the induced homomorphism R/m→ S/mS is …

R be a commutative graded Noetherian ring. It is well-known that Artinian modules have
secondary representations. We prove that the same holds also for any projective R-module …

One can try to generalize this result to (unital left) modules A over a ring with 1, by replacing
torsion-freeness and freeness by flatness and projectivity, respectively. One naturally …

Suppose (R, m)→(S, n) is a local homomorphism of local rings. We show that if M is a Matlis
reflexive R-module, then R (S, M) and TorR (S, M) are Matlis reflexive S-modules if S is …

The main theorem of the paper" Flatness and Injectivity of Simple Modules over a
Commutative Ring" by Xu Jinzhong which appeared in Communications in Algebra 19 (2) …

We studied almost relative projective modules and almost relative injective modules in [3, 6,
7]. In this short note we define a new module, an almost projective (resp. almost injective) …

B. Maddox [15] defined absolutely pure modules and derived some interesting properties of
these modules. C. Megibben [17] continued the study of these modules and found more …