Let ${} _RM $ be a left $ R $-module whose Morita context is nondegenerate, $ S={\text
{End}}({} _RM) $, and $ N=\operatorname {Hom}({} _RM, R) $. If ${} _RM $ is also …

Let $ M $ be a non-zero finitely generated module over a finite dimensional commutative
Noetherian local ring $(R,\mathfrak {m}) $ with dim $ _R (M)= t $. Let $ I $ be an ideal of $ R …

Let R be a ring, and let (ℐ, ℱ) be an hereditary torsion theory of left R-modules. An
epimorphism ψ: M→ X is called a torsion-free cover of X if (1) M∈ ℱ,(2) every …

2. Uniqueness Problem. If R, S e 3,„M,, N e. and End („M)== End (N), what can be said about
the relationship between R and S,„M and, Nº More precisely, is it true that R2= S and that …

We study the notions of n-hereditary rings and its connection to the classes of finitely n-
presented modules, FP n-injective modules, FP n-flat modules and n-coherent rings. We …

Let R be a ring. A right R-module M is said to be neat-flat if the kernel of any epimorphism Y-
> M is neat in Y, ie, the induced map Hom (S, Y)-> Hom (S, M) is surjective for any simple …

Chapter 1 covers the background necessary for what follows. In particular, general
properties of injectivity and some of its well-known generalizations are stated. Chapter 2 is …

REGULAR ENDOMORPHISMS OF FINITELY GENERATED MODULES Page 1 REGULAR
ENDOMORPHISMS OF FINITELY GENERATED MODULES WOLMER V. VASCONCELOS …

For any ring A and left (resp. right)^.-module E we let E* denote the right (resp, left) A-
module HomA {E, A8)(resp. Hom^(E, Ad)) where A8 (resp. Ad) denotes A considered as a …

Let R be a reduced, one-dimensional Noetherian local ring whose integral closure R is
finitely generated over R. Since R is a direct product of finitely many principal ideal domains …