Let C ⊂ Z be an affine semigroup, R = K[C] its semigroup ring, and *modC R the category of finitely generated “C-graded” R-modules (i.e., Z -graded modules M with M = ⊕ c∈C Mc). When R is Cohen-Macaulay and simplicial, we show that information on M ∈ *modC R such as depth, CohenMacaulayness, and (Sn) condition, can be read off from numerical invariants of the minimal irreducible resolution (i.e...

Abstract We consider the dominant dimension of an order over a Cohen-Macaulay ring in category centrally modules. There is canonical tilting module case positive and we give upper bound on global its endomorphism ring.

We introduce the notion of mutation on the set of n-cluster tilting subcategories in a triangulated category with Auslander-Reiten-Serre duality. Using this idea, we are able to obtain the complete classifications of rigid Cohen-Macaulay modules over certain Veronese subrings.

Introduction. In [1], the Koszul complex was used to study the relationship between codimension and multiplicity. It also helped us investigate Macaulay modules and rings, and provided a context in which to prove the Cohen-Macaulay Theorem concerning the unmixedness of complete intersections. Now there is a generalization of the Cohen-Macaulay Theorem (known, we believe, as the generalized Cohe...

We introduce the notion of mutation on the set of n-cluster tilting subcategories in a triangulated category with Auslander-Reiten-Serre duality. Using this idea, we are able to obtain the complete classifications of rigid Cohen-Macaulay modules over certain Veronese subrings.

The nilpotent endomorphisms over a finite free module over a domain with principal ideal are characterized. One may apply these results to the study of the maximal Cohen-Macaulay modules over the ring R := A[[x]]/(x), n ≥ 2, where A is a DVR. Subject Classification: 15A21, 13C14.

We generalise Yoshino’s definition of a degeneration of two Cohen Macaulay modules to a definition of degeneration between two objects in a triangulated category. We derive some natural properties for the triangulated category and the degeneration under which the Yoshino-style degeneration is equivalent to the degeneration defined by a specific distinguished triangle analogous to Zwara’s charac...

Formulas are obtained in terms of complete reductions for the bigraded components of local cohomology modules of bigraded Rees algebras of 0-dimensional ideals in 2-dimensional Cohen-Macaulay local rings. As a consequence, cohomological expressions for the coefficients of the Bhattacharya polynomial of such ideals are obtained.

In this paper, we use a characterization of R-modules N such that fdRN = pdRN to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting N to be the dth local cohomology functor of R with respect to the maximal ideal where d is the Krull dimension of R.