In this paper, the notion of strongly G_C-projective and injective modules is introduced,
where C is a semidualizing module. Using these modules we can obtain a new …

We prove that (a) if R is a commutative coherent ring, the weak global dimension of R equals
the supremum of the flat (or (FP–) injective) dimensions of the simple R-modules;(b) if R is …

Let $ R $ be a ring, $ n $ be an non-negative integer and $ d $ be a positive integer or $\infty
$. A right $ R $-module $ M $ is called\emph {$(n, d)^* $-projective} if ${\rm Ext}^ 1_R (M …

In this note, we show that a ring $ R $ is $ S $-coherent if and only if every finitely presented
$ R $-module is $ S $-coherent, providing a positive answer to a question proposed in [D …

The present paper aims at seeking the Hilbert syzygies' theorem for the power series ring R
[[t]] with respect to the global dimension as well as the weak global dimension. Actually, our …

This paper introduces and studies homological properties of new classes of modules,
namely, the $\mathcal F_1 $-flat modules and the $\mathcal F_1^{\fp} $-flat modules, where …

Let R be a ring and R ω a self-orthogonal module. We introduce the notion of the right
orthogonal dimension (relative to R ω) of modules. We give a criterion for computing this …

Let R be a ring. A subclass T of left R-modules is called a weak torsion class if it is closed
under homomorphic images and extensions. Let T be a weak torsion class of left R-modules …

ON N-COHERENT RINGS, N-HEREDITARY RINGS AND N-REGULAR RINGS Page 1 Archive
of SID Bulletin of the Iranian Mathematical Society Vol. 37 No. 4 (2011), pp 251-267. ON …