… In particular, it is proven that the injective envelope of any projective left R-module is
projective if and only if the class of quotient-modules of projective and injective left R-modules is …

… Given an R-module C and a class of R-modules D over a … the existence of D-envelopes
(respectively, D-covers) and the … Let A be a quotient of a C-injective R-module B. Since A has …

… We let 2 denote multiplication by 2 and nat the natural homomorphism from a module to its
quotient by a submodule (that is, it sends each element to the equivalence class containing it)…

… F-envelopes or 3-covers. It follows … K-module has a monomorptiic projective envelope are
the QF rings, while the ,-ings for which every left R-module has a rnonomorphic free envelope, …

… covers and of cotorsion envelopes in the sense of Enochs, Warfield and Matlis. We also
construct approximations by modules … domain then Q coincides with the quotient field of R. Let R …

… of injective modules, then we get the usual injective envelopes. … R-module has a flat envelope
we know that R is right … M* has a flat envelope, and so M** has a projective cover by [1, …

… )covers and (pre)envelopes are important notions in relative homological algebra. For example,
let R be a ring, given a precovering class F , then for any R-module … and pure quotients, it …

… In this chapter we define envelopes and covers for a given class of modules and study their
… Then the natural surjection y : Ŕ → R/m is a torsion free covering of the quotient field k = R/m (…

Chapter 1 Envelopes and Covers Page 1 Chapter 1 Envelopes and Covers In this chapter we
define envelopes and covers for a given class of modules and study their basic properties. …

… covers and envelopes by some special functors on the category of finitely presented modules.
… By Proposition 2.7, F is a quotient of an FP-injective functor. But F has a monic FP-injective …