We consider the possibility of characterizing Buchsbaum and some special generalized Cohen-Macaulay rings by systems of parameters having certain properties of regular sequences. As an application, we give a bound on Castelnuovo-Mumford regularity of so-called (k, d)-Buchsbaum graded Kalgebras.

We investigate the transfer of the Cohen-Macaulay property from a commutative ring to a subring of invariants under the action of a finite group. Our point of view is ring theoretic and not a priori tailored to a particular type of group action. As an illustration, we briefly discuss the special case of multiplicative actions, that is, actions on group algebras k[Z n ] via an action on Z n .

We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine semigroup rings, and characterizing linear resolutions of squarefree monomial ideals. The characterization in the graded setting is via the Cohen-Macaulay property of certain posets or simplicial complexes, and in the mo...

Let R be a local Cohen-Macaulay ring, I an R-ideal and G the associated graded ring of I. We give an estimate for the depth of G when G fails to be Cohen-Macaulay. We assume that I has small reduction number, sufficiently good residual intersection properties, and satisfies local conditions on the depth of some powers. The main theorem unifies and generalizes several known results. We also give...

The so-called ’change-of-ring’ results are well-known expressions which present several connections between projective, injective and flat dimensions over the various base rings. In this note we extend these results to the Gorenstein dimensions over Cohen-Macaulay local rings.

The so-called ’change-of-ring’ results are well-known expressions which present several connections between projective, injective and flat dimensions over the various base rings. In this note we extend these results to the Gorenstein dimensions over Cohen-Macaulay local rings.

In this paper, we investigate the maximal Cohen-Macaulay property of tensor products modules, and then give criteria for projectivity modules in terms vanishing Ext modules. One applications shows that Auslander-Reiten conjecture holds normal rings.