In the last two decades Cohen-Macaulay rings and modules have been central topics in
commutative algebra. This book meets the need for a thorough, self-contained introduction …

In this paper, we study a Noetherian graded ring R and the category of graded R-modules.
We consider injective objects of this category and we define the graded Cousin complex of a …

The notion of the trivial or split extension of a ring by a bimodule has played an important
role in various parts of algebra. In most cases, however, it is introduced ab initio and then …

A characterization is given of those Noetherian rings $ R $ such that whenever $ R $ is
ideally closed ($\equiv $ cyclically pure) in an extension algebra $ S $, then $ R $ is pure in …

CERTAIN INVARIANT SUBRINGS ARE GORENSTEIN II Page 1 Watanabe, K. Osaka J. Math.
11 (1974), 379-388 CERTAIN INVARIANT SUBRINGS ARE GORENSTEIN II KEIICHI …

Since Bass' original paper [5] on injective resolutions and Gorenstein rings, there has been
a number of papers following a similar theme. Perhaps the most notable is the paper of …

Homological algebra had its origins in the 19th century, via the work of Riemann (1857) and
Betti (1871) on “homology numbers,” and the rigorous development of the notion of …

Let A be a Noetherian local ring with canonical module K. We characterize A when K is a
torsionless, reflexive, or q-torsionfree module. If A is a Cohen-Macaulay ring, H.-B. Foxby …

0-* M-> E-^ E1...-> Ei... be a minimal injective resolution of M, that is, Ei is the injective en
velope of Kerdi= Imdi_1 for all i. Then the cardinal number μί (ρ, Μ), where p is a prime ideal …

Let R be a commutative noetherian local ring. A finitely generated R-module C is
semidualizing if it is self-orthogonal and\rm Hom _R (C, C) ≅ R. We prove that a Cohen …