Let [Formula: see text] where be a complete regular local ring of dimension text], for some and an MCM text]-module with then we prove that text]. If is hypersurface infinite residue field let or Our paper the first systematic study depth associated graded modules over rings.

We show that symmetry in the vanishing of cohomology holds for graded modules over quantum complete intersections. Moreover, symmetry holds for all modules if the algebra is symmetric.

This paper explains the relation between the fusion product of symmetric power sln evaluation modules, as defined by Feigin and Loktev, and the graded coordinate ring Rμ which describes the cohomology ring of the flag variety Flμ′ of GLN . The graded multiplicity spaces appearing in the decomposition of the fusion product into irreducible sln-modules are identified with the multiplicity spaces ...

Consider a coring with exact rational functor, and a finitely generated and projective right comodule. We construct a functor (coinduction functor) which is right adjoint to the hom-functor represented by this comodule. Using the coinduction functor, we establish a bijective map between the set of representative classes of torsion simple right comodules and the set of representative classes of ...

The behaviour under coarsening functors of simple, entire, or reduced graded rings, free modules over principal superfluous monomorphisms and homological dimensions modules, as well adjoints degree restriction functors, are investigated.

Bounds for the Castelnuovo-Mumford regularity of Ext modules, over a polynomial ring over a field, are given in terms of the initial degrees, Castelnuovo-Mumford regularities and number of generators of the two graded modules involved. These general bounds are refined in the case the second module is the ring. Other estimates, for instance on the size of graded pieces of these modules, are give...

Abstract. We use the results by Eisenbud and Schreyer [3] to prove that any Betti diagram of a graded module over a standard graded polynomial ring is a positive linear combination Betti diagrams of modules with a pure resolution. This implies the Multiplicity Conjecture of Herzog, Huneke and Srinivasan [5] for modules that are not necessarily Cohen-Macaulay. We give a combinatorial proof of th...

In 1982 Richard P. Stanley conjectured that any finitely generated Zn-graded module M over a finitely generated Nn-graded K-algebra R can be decomposed as a direct sum M = ⊕t i=1 νi Si of finitely many free modules νi Si which have to satisfy some additional conditions. Besides homogeneity conditions the most important restriction is that the Si have to be subalgebras of R of dimension at least...