… in the subcategory of all finitely generated modules. So the … : each module has a flat cover
and a cotorsion envelope, [25]. … A ring R is called Iwanaga-Gorenstein provided that R is left …

… an X-cover if every R-morphism ψ : X → X satisfying ϕ = ϕψ is … we have the definitions of an
X-(pre)envelope and an X-(pre)… coherent ring with NB and MA finitely generated projective. (1…

… We show that there is a finitely generated product-complete … is perfect if every module has
an A-cover and a B-envelope. … as it also satisfies the ascending chain condition for finite matrix …

… -dimension zero, denoted G-dimR G º 0, if it is reflexive and satisfies … Gorenstein rings every
finitely generated module has finite G-dimension. Using this fact we describe GTfi, modules …

… by using the class of Gorenstein projective modules. In order to … a (module) homomorphism
from M to M if it satisfies the … In particular, we also have the concept of a finitely generated …

… cover of − ⊗M in (mod-R, Ab), it is enough to check that any morphism satisfying the …
Recall that a ring R is right coherent if every finitely generated right ideal is finitely presented…

… , the class of so-called Gorenstein projective modules is pre-covering. … -pre-envelope.
These can be checked by first noting that the compact modules are exactly the finitely generated …

… rings is called a Frobenius extension if R is finitely generated and projective as a left S-module …
→ 1D of the adjunction satisfy the identities εF (X)F(ηX )=1F (X) and G(εY )ηG(Y ) = 1G(Y ) …

… We show (Theorem 4.2) that a ring R is left n-perfect if and only if every Gorenstein flat left
R-… Perfect if every module has an X-cover and a Y-envelope. • Cogenerated by a set if there is …

… of which (including basic facts about preradicals, torsion theories, injective envelopes, Gabriel
… (8) R is Noetherian if every ideal of R is finitely generated, or equivalently if R satisfies the …