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 …

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 …

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) …

Module theory provides a general framework for the study of linear representations of
various mathematical objects. For example, given a field K, representations of a quiver Q …

Let R be a ring, na fixed non-negative integer and ℱ ℐ n (ℱ n) the class of all right (left) R-
modules of FP-injective (flat) dimension at most n. We prove that (is a perfect cotorsion …

We show that if the given cotorsion pair in the category of modules is complete and
hereditary, then both of the induced cotorsion pairs in the category of complexes are …

Abstract We study Gorenstein categories. We show that such a category has Tate
cohomological functors and Avramov–Martsinkovsky exact sequences connecting the …

However, some aspects of the classical theory can be extended to infinitely generated
modules over arbitrary rings. In this paper, we will consider such an aspect: the relation of …

We apply the theory of cotorsion pairs to study closure properties of classes of modules with
finite projective dimension with respect to direct limit operations and to filtrations. We also …

Let RR be a commutative Noetherian ring. For a natural number kk, we prove that the class
of modules of projective dimension bounded by kk is of finite type if and only if RR satisfies …