This paper presents the right-left symmetry of the CS and max-min CS conditions on
nonsingular rings, and generalization to nonsingular modules. We prove that a ring is right …

Let m and n be fixed positive integers and M a right R-module. Recall that M is said to be (m,
n)-injective if for any (m, n)-presented right R-module P; M is called (m, n)-flat if for any (m, n) …

We show that the small and large restricted injective dimensions coincide for Cohen-
Macaulay rings of finite Krull dimension. Based on this, and inspired by the recent work of …

Let R be a commutative Noetherian ring of dimension d and M a commutative cancellative
torsion-free seminormal monoid. Then:(1) Let A be a ring of type R [d, m, n] and P be a …

Let $ R $ be a commutative ring. An $ R $-module $ M $ is said to be $ w $-flat if $\Tor^{R} _
{1}(M, N) $ is $ GV $-torsion for any $ R $-module $ N $. It is known that every flat module is …

Let R be a left Noetherian ring, S a right Noetherian ring and R ω a Wakamatsu tilting
module with S= End (R ω). We introduce the notion of the ω-torsionfree dimension of finitely …

Let $ A $ be a commutative noetherian ring, $\frak a $ be an ideal of $ A $, $ m, n $ be non-
negative integers and let $ M $ be an $ A $-module such that $\Ext^ i_A (A/\frak a, M) $ is …

Abstract Let T=(A 0 UB) be a formal triangular matrix ring, where A and B are rings and U is
a (B, A)-bimodule. Let C 1 and C 2 be two classes of left A-modules, D 1 and D 2 be two …

Let R be a strong n-coherent ring such that each finitely n-presented R-module has finite
projective dimension. We consider ℱ 𝒫 n (R) the full subcategory of R-Mod of finitely n …

Let (A, B) be a cotorsion pair in R-Mod. We define and study notions of A dimension and B
dimension of unbounded complexes, which is given by means of dg-projective resolution …