This paper studies the class of rings in which every finitely projective ideal is projective (FPP-
ring for short). We examine the transfer of this property to various context of commutative ring …

If R is a valuation domain of maximal ideal P with a maximal immediate extension of finite
rank it is proven that there exists a finite sequence of prime ideals P= L0⊃ L1⊃⋯⊃ Lm⊇ 0 …

Let R be a ring and I an ideal of R. We define and study I-pure submodules, I-FP-injective
modules, I-flat modules, I-coherent rings and I-semihereditary rings. Using the concepts of I …

Let R be a ring, let I be an ideal of R, and let n be a fixed positive integer. We define and
study In-injective modules and In-flat modules. Moreover, we define and study left In …

Let $ R $ be a commutative ring with nonzero identity. An $ R $-module $ M $ is called $\phi
$-P-flat if $ x\in\Ann (s) M $ for every non-nilpotent element $ s\in R $ and $ x\in M $ such …

Let R be a ring and 𝑆 be a class of some finitely generated left R-modules. Then a left R-
module M is called 𝑆-projective if for every homomorphism f: S→ M, where S∈ 𝑆, there exist …

In this paper, several characterizations of semi-compact modules are given. Among other
results, we study rings whose semi-compact modules are injective. We introduce the …

Let I be an ideal of a ring R. We call R weakly I-semiregular if R/I is a von Neumann regular
ring. This definition generalizes I-semiregular rings. We give a series of characterizations …

Let R be a commutative ring. We define and study f-projective modules with respect to a
semidualizing R-module C, which are called C–f-projective modules. As consequences, we …