We show that any quasi-Gorenstein deformation of a 3-dimensional Buchsbaum local ring with I-invariant 1 admits maximal Cohen-Macaulay module, provided it is quotient Gorenstein ring. Such class rings includes two instances unique factorization domains constructed by Marcel-Schenzel and Imtiaz-Schenzel, respectively. Apart from this result, motivated the small conjecture in prime characteristic...

Let (R,m) be a commutative Noetherian local ring. Suppose that M and N are finitely generated modules over R such that M has finite projective dimension and such that TorRi (M,N) = 0 for all i > 0. The main result of this note gives a condition on M which is necessary and sufficient for the tensor product of M and N to be a Cohen–Macaulay module over R, provided N is itself a Cohen–Macaulay mod...

A few years ago, Huneke and Leuschke proved a theorem which solved a conjecture of Schreyer. It asserts that an excellent Cohen-Macaulay local ring of countable Cohen-Macaulay type which is complete or has uncountable residue field has at most a one-dimensional singular locus. In this paper, it is verified that the assumption of the excellent property can be removed, and the theorem is consider...

We introduce the notion of residual intersections modules and prove their existence. show that projective dimension one have Cohen-Macaulay intersections, namely they satisfy relevant Artin-Nagata property. then establish a formula for core orientable satisfying certain homological conditions, extending previous results Corso, Polini, Ulrich on modules. Finally, we provide examples classes our ...

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...

We give conjectures on the possible graded Betti numbers of Cohen-Macaulay modules up to multiplication by positive rational numbers. The idea is that the Betti diagrams should be non-negative linear combinations of pure diagrams. The conjectures are verified in the cases where the structure of resolutions are known, i.e., for modules of codimension two, for Gorenstein algebras of codimension t...

The main theorem of this paper complements the tame-wild dichotomy for commutative Noetherian rings, obtained by Klingler and Levy [14]–[16]. They gave a complete classification of all finitely generated modules over Dedekind-like rings (cf. Definition 1.1) and showed that, over any ring that is not a homomorphic image of a Dedekind-like ring, the category of finite-length modules has wild repr...

The Grothendieck-Serre formula for the difference between the Hilbert function and Hilbert polynomial of a graded algebra is generalized for bigraded standard algebras. This is used to get a similar formula for the difference between the Bhattacharya function and Bhattacharya polynomial of two m-primary ideals I and J in a local ring (A, m) in terms of local cohomology modules of Rees algebras ...

This paper considers the following conjecture: If R is an unmixed, equidimensional local ring that is a homomorphic image of a Cohen-Macaulay local ring, then for any ideal J generated by a system of parameters, the Chern coefficient e1(J) < 0 is equivalent to R being non Cohen-Macaulay. The conjecture is established if R is a homomorphic image of a Gorenstein ring, and for all universally cate...