Let R be a left coherent ring, FP—idRR the FP—injective dimension of RR and wD (R) the
weak global dimension of R. It is shown that 1) FP-idRR< n (n> 0) if and only if every flat …

For a ring D and a subring C, let ℛ [D, C]={(d 1,…, dn, c, c,…): di∈ D, c∈ C, n≥ 1}, a subring
of, and let, a subring of 𝕄2 (D). In this article, various conditions are obtained for ℛ [D, C] and …

ABSTRACT A module M is called strongly FP-injective if Ext i (P, M)= 0 for any finitely
presented module P and all i≥ 1.(Pre) envelopes and (pre) covers by strongly FP-injective …

A ring R is called left “GF-closed”, if the class of all Gorenstein flat left R-modules is closed
under extensions. The class of left GF-closed rings includes strictly the one of right coherent …

In this paper, we show the existence of copure injective preenvelopes over noetherian rings
and copure flat preenvelopes over commutative artinian rings. We use this to characterize …

A right R-module UR is said to be cotilting if Cog (UR)=⊥ UR, where⊥ UR= KerExt1R (, U).
So cotilting modules generalize injective cogenerators. If U is cotilting, then T=(KerHom …

In § 1, we begin with a basic theorem which describes a convenient embedding of a
nonsingular left R-module into a complete direct product of copies of the left injective hull of …

In this paper, we continue to study and investigate the homological objects related to s-pure
and neat exact sequences of modules and module homomorphisms. A right module A is …

In this note we characterize those torsion theories over a semiperfect ring such that the class
of torsion free modules is closed under projective covers and the hereditary torsion theories …

If M and N are right R-modules, M is called simple-N-injective if every R-homomorphism γ
from a submodule K of N into M with γ (K) simple extends to N. In this paper, a right R …