In basic homological algebra, the projective, injective and flat dimensions of modules play
an important and fundamental role. In this paper, the closely related Gorenstein projective …

There are different approaches to characterizing the structures of commutative rings: the
category of modules over commutative rings, homology theories, theories of the star …

References Page 1 References [1] S. Abhyankar, S. Wiegand, On the compositum of two power
series rings, Proc. Amer. Math. Soc. 112 (1991), 629 – 636. [2] U. Albrecht, Endomorphism …

This book is a comprehensive treatment of the representation theory of maximal Cohen-
Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative …

In this paper the authors investigate homological and homotopical aspects of a concept of
torsion which is general enough to cover torsion and cotorsion pairs in abelian categories …

for a noetherian scheme, we introduce its unbounded stable derived category. this leads to a
recollement which reflects the passage from the bounded derived category of coherent …

We make a general study of Quillen model structures on abelian categories. We show that
they are closely related to cotorsion pairs, which were introduced by Salce [Sal79] and have …

This book provides a comprehensive exposition of the use of set-theoretic methods in
abelian group theory, module theory, and homological algebra, including applications to …

Given a cotorsion pair $(\mathcal {A},\mathcal {B}) $ in an abelian category $\mathcal {C} $
with enough $\mathcal {A} $ objects and enough $\mathcal {B} $ objects, we define two …

Over the last few years, the study of complexes has become increasingly important. To date,
however, most of the research is scattered throughout the literature or available only as …