In this paper, we first study $ fs $-modules, ie, modules with finitely many small submodules.
We show that every $ fs $-module with finite hollow dimension is Noetherian. Also, we prove …

Let $ R $ be a commutative ring with identity and $ S $ a multiplicative subset of $ R $. First,
we introduce and study the $ u $-$ S $-projective dimension and $ u $-$ S $-injective …

PM Cohn [3] has introduced the notion of purity for R-modules. With respect to purity, flat,
absolutely pure and regular modules are studied. In this paper we introduce and study the …

The notion of ω-k-torsionfree modules with respect to a bimodule ω is introduced, which is
characterized in terms of left add R ω-approximations. The notion of ω-left approximation …

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 …

In this paper, we study left orthogonal class of max-flat modules which are the homological
objects related to s-pure exact sequences of modules and module homomorphisms …

Let R be a discrete valuation domain with field of fractions Q and maximal ideal generated
by. Let be an R-order such that is a separable Q-algebra. Maranda showed that there exists …

This paper focuses on the study of φ-weak global dimensions in the context of polynomial
rings and φ-Prüfer rings. We explore new properties of these dimensions and extend the …

Given modules X and Y, X is said to be Y-subprojective if for every epimorphism\(\pi:
P\rightarrow Y\) and every homomorphism\(\alpha: X\rightarrow Y\), there exists a …