This book has evolved out of a graduate course in algebra I gave at Brandeis University
during the academic year of 1967-1968. At that time M. Auslander taught algebraic geometry …

The Rees algebra is the homogeneous coordinate ring of a blowing-up. The present paper
gives a necessary and sufficient condition for a Noetherian local ring to have a Cohen …

The best known theorems of this type assert the conservation o the Gorenstein property
under the formation of generic hypersurf sections or of flat families with Gorenstein fibers. In …

In this paper, we prove Faltings' annihilator theorem for complexes over a CM-excellent ring.
As an application, we give a complete classification of the t-structures of the bounded …

We establish the Local-global Principle for the annihilation of local cohomology modules
over an arbitrary commutative Noetherian ring R at level 2. We also establish the same …

Let P be a property of local rings. The P-locus of a ring A is the set Up (A) consisting of those
peSpec (A) such that Ap has property P. A natural question is the following: when is Ue (A) …

In this paper, we consider the openness of the P-locus of a finitely generated module over a
commutative noetherian ring in the case where P is each of the properties FID, Gor, Can …

§ . O. Introduction: Dualizing complexes were introduced in 1963/4 by Grothendieck and
Hartshorne in [6; Chapter V] for use in algebraic geometry. However, in recent years, it has …

Throughout this paper the word 'ring'will mean 'commutative Noetherian ring with non-zero
identity', and A will always denote such a ring. It will only be assumed that A is local when …

The notion of the Cousin complex of a module was given by Sharp in 1969. It wasn't known
whether its cohomologies are finitely generated until recently. In 2001, Dibaei and Tousi …