Related papers: On strongly $\phi$-$w$-Flat modules and Their Homo…

In this paper, we introduce and study the class of $\phi$-$w$-flat modules which are generalizations of both $\phi$-flat modules and $w$-flat modules. The $\phi$-$w$-weak global dimension $\phi$-$w$-w.gl.dim$(R)$ of a strongly $\phi$-ring…

In this paper, we first introduce and study the notions of strongly $\phi$-flat modules and strongly nonnil-injective modules. And then, we investigate the homology dimensions of modules and rings in terms of these two notions. Finally we…

In this paper, we introduce and study the class of $\phi$-$w$-P-flat modules, which can be seen as generalizations of both $\phi$-P-flat modules and $w$-P-flat modules. In particular, we obtain that the class of $\phi$-$w$-P-flat modules is…

Let R be a commutative ring with identity, and let S be a multiplicative subset of R. Positselski and Sl\'avik introduced the concepts of S-strongly flat modules and S-weakly cotorsion R-modules, and they showed that these concepts are…

In this paper, we introduce and study the $S$-weak global dimension $S$-w.gl.dim$(R)$ of a commutative ring $R$ for some multiplicative subset $S$ of $R$. Moreover, commutative rings with $S$-weak global dimension at most $1$ are studied.…

Let $R$ be a ring and $n$, $k$ two non-negative integers. In this paper, we introduce the concepts of $n$-weak injective and $n$-weak flat modules and via the notion of special super finitely presented modules, we obtain some…

Let $R$ be a ring. An $R$-module $M$ is said to be an absolutely $w$-pure module if and only if $\Ext^1_R(F,M)$ is a GV-torsion module for any finitely presented module $F$. In this paper, we introduce and study the concept of…

Let $R$ be a commutative ring. An $R$-module $M$ is called a semi-regular $w$-flat module if $\Tor_1^R(R/I,M)$ is $\GV$-torsion for any finitely generated semi-regular ideal $I$. In this article, we show that the class of semi-regular…

In this paper we characterize the relative Gorenstein weak global dimension of the generalized Gorenstein $\mathrm{FP}_n$-flat $R$-modules and Projective Coresolved $\mathrm{FP}_n$-flat $R$-modules recently studied by S. Estrada, A. Iacob,…

Let $R$ be a commutative ring. An $R$-module $M$ is said to be $w$-split if Ext$_{R}^1(M,N)$ is a GV-torsion $R$-module for all $R$-modules $N$. It is known that every projective module is $w$-split, but the converse is not true in general.…

Let $R$ be a ring. An $R$-module $M$ is said to be a weak $w$-projective module if ${\rm Ext}_R^1(M,N)=0$ for all $N \in \mathcal{P}_{w}^{\dagger_\infty}$ (see, \cite{FLQ}). In this paper, we introduce and study some properties of weak…

In this note, we show that a strongly $\phi$-ring $R$ is a $\phi$-PvMR if and only if any $\phi$-torsion free $R$-module is $\phi$-$w$-flat, if and only if any divisible module is nonnil-absolutely $w$-pure module, if and only if any…

We first introduce and study the notion of semi-regular flat modules, and then show that a ring $R$ is a strong \Prufer\ ring if and only if every submodule of a semi-regular flat $R$-module is semi-regular flat, if and only if every ideal…

In this paper, the $\tau_q$-weak global dimension $\tau_q$-\cwd$(R)$ of a commutative ring $R$ is introduced. Rings with $\tau_q$-weak global dimension equal to $0$ are studied in terms of homologies, direct products, polynomial extensions…

In this paper we introduce and study the weak Gorenstein global dimension of a ring $R$ with respect to a left $R$-module $C$. We provide several characterizations of when this homological invariant is bounded. Two main applications are…

In this study, we introduce graded pseudo weakly prime submodules of G-graded R-modules, which are an extension of graded weakly prime ideals over G-graded rings. On the graded spectrum of graded pseudo weakly prime submodules, we…

In \cite{Ouarghi}, the authors discuss the rings over which all modules are strongly Gorenstein projective. In this paper, we are interesting to an extension of this idea. Thus, we discuss the rings over which every Gorenstein projective…

In this paper, we define a class of relative derived functors in terms of left or right weak flat resolutions to compute the weak flat dimension of modules. Moreover, we investigate two classes of modules larger than that of weak injective…

In this paper, we study the small finitistic dimension of a commutative ring from the viewpoint of finitistic flat homological algebra. Using the class $FPR(R)$ of modules admitting finite projective resolutions, we investigate the…

In this paper, we first study the Gorenstein projective/flat dimension of complexes of modules. The relation between the Gorenstein projective/flat dimension for complexes and that for modules are investigated. Then we study Tate, stable…