Let R be an arbitrary ring and let (−)+= HomZ (−, Q/Z), where Z is the ring of integers and Q is
the ring of rational numbers. Let C be a subcategory of left R-modules and D a subcategory …

Through concepts from non-commutative algebra and homology, this paper resolves the
conjecture that lets the first bifunctor extension to be zero when the projective dimension is …

Let R be a ring and M a right R-module. Let σ [M] be the full subcategory of Mod-R
subgenerated by M. An M-natural class 𝒦 is a subclass of σ [M] closed under submodules …

An R-module M is said to satisfy ACC d (resp. DCC d) on submodules if for every ascending
(resp. descending) chain {M i} of submodules of M, M i= φ i (M i+ 1)(resp. M i+ 1= φ i (M i)) for …

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 …

Bazzoni and Salce have showed that all modules over a commutative domain R have a
strongly flat cover if and only if every flat R-module is strongly flat and that holds if and only if …

RINGS OVER WHICH FLAT COVERS OF SIMPLE MODULES ARE PROJECTIVE Page 1
Journal of Algebra and Its Applications Vol. 11, No. 3 (2012) 1250046 (7 pages) c© World …

Let R, S be arbitrary associative rings and RCS a semidualizing bimodule. We give some
equivalent characterizations for R being left coherent (and right perfect) rings, left …

In generalizing the well-established notion of projective cover, the notions of D3-cover and
rad-projective cover were recently introduced and new characterizations of perfect and …

We show that a weak-injective module over an integral domain need not be pure-injective
(Theorem 2.3). Equivalently, a torsion-free Enochs-cotorsion module over an integral …