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 …

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 …

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 …

In this paper, we study a particular case of Gorenstein projective, injective, and flat modules,
which we call, respectively, strongly Gorenstein projective, injective, and flat modules. These …

A quantum symmetric pair consists of a quantum group U $\mathbf {U} $ and its coideal
subalgebra U ς ı ${\mathbf {U}}^{\imath} _ {\bm {\varsigma}} $ with parameters ς $\bm …

We introduce compatible bimodules. If M is a compatible A–B-bimodule, then the Gorenstein-
projective modules over algebra Λ=(AM0B) are explicitly described; and if Λ is Gorenstein …

We use torsion pairs in stable categories and cotorsion pairs in modules categories to study,
in general infinitely generated, Cohen–Macaulay modules and (a generalization of) …