In this paper we extend the notion of FP-injective modules to that of complexes and
characterize such complexes. We show that some characterizations similar to those for …

By defining orthogonal decomposition for modules, we prove that an R-module M has only
finitely many fully invariant direct summands if and only if End R (M) has triangulating …

Let $ R $ be a ring, $ n $ a fixed non-negative integer, ${\mathscr {WI}} $ the class of all left $
R $-modules with weak injective dimension at most $ n $, and ${\mathscr {WF}} $ the class …

Abstract A ring\(R\) is said to be a left\(IF-(m, n)\) ring if every injective left\(R\)-module is\((m,
n)\)-flat. In this paper, several characterizations of left\(IF-(m, n)\) rings are investigated, some …

Let R be a noetherian ring and S an excellent extension of R. cid (M) denotes the copure
injective dimension of M and cfd (M) denotes the copure flat dimension of M. We prove that if …

Let $ R $ be a ring, $ S $ a multiplicative subset of $ R $. An $ R $-module $ M $ is said to
be $ u $-$ S $-flat ($ u $-always abbreviates uniformly) if $\Tor^ R_1 (M, N) $ is $ u $-$ S …

Let A and B be rings and U a (B, A)-bimodule. If BU is flat and UA is finitely generated
projective (resp., BU is finitely generated projective and UA is flat), then the characterizations …

Let M be a right R-module,(S,≤) a strictly totally ordered monoid which is also artinian and
ω: S−→ Aut (R) a monoid homomorphism, and let [MS,≤][[RS,≤, ω]] denote the generalized …

Let R be a commutative ring. An R-module M is said to be w-flat if TorR 1 (M, N) is a GV-
torsion R-module for all R-modules N. In this paper, we study the flat and projective …

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 …