This is the second revised edition of an introduction to contemporary relative homological
algebra. It supplies important material essential to understand topics in algebra, algebraic …

Since the injective envelope and projective cover were defined by Eckmann and Bas in the
1960s, they have had great influence on the development of homological algebra, ring …

In this paper, strongly Gorenstein flat modules are introduced and investigated. An R-
module M is called strongly Gorenstein flat if there is an exact sequence⋯→ P1→ P0→ P0→ …

After the introduction hy Enochs [9] of the concepts of (pre) erlveIope and I llrejcover of a
module 1r1 a gi\wi class F of modules, there has been great interest in tllelr stud;, specially …

We prove that (a) if R is a left coherent ring, then the weak global dimension w D (R)<= n
(n>= 2) if and only if every (n–2) th F–cosyzygy of a finitely presented right R–module has a …

Let R be a ring, na fixed non-negative integer and ℱ ℐ n (ℱ n) the class of all right (left) R-
modules of FP-injective (flat) dimension at most n. We prove that (is a perfect cotorsion …

Relative coherence and preenvelopes Page 1 manuscripta math. 81, 243- 262 (1993)
manuscripta mathematica 9 Springer rlag 1993 RELATIVE COHERENCE AND …

All the rings will be associative with identity and the modules will be unital. If M is a right
module we denote by M* the dual module Hom „(M., R) of M. If M is a right R-module, a flat …

We prove the following results for a ring R.(a) If C is a class of right R-modules closed under
direct summands and isomorphisms, then every right R-module has an epic C-envelope if …

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) …