This paper shows that if [Formula: see text] is a homomorphic image of Cohen–Macaulay local ring, then text]-module sequentially generalized and only the difference between Hilbert coefficients arithmetic degrees for all distinguished parameter ideals are bounded.

The arithmetic degree, the smallest extended degree, and the homological degree are invariants that have been proposed as alternatives of the degree of a module if this module is not Cohen-Macaulay. We compare these degree functions and study their behavior when passing to the generic initial or the lexicographic submodule. This leads to various bounds and to counterexamples to a conjecture of ...

In this paper, we consider a finite, torsion-free module E over Gorenstein local ring. We provide sufficient conditions for to be of linear type and the Rees algebra R ( ) Cohen-Macaulay. Our results are obtained by constructing generic Bourbaki ideal I exploiting properties residual intersections .

In the winter of 1999 I gave a series of lectures at Queen’s university about some recent results concerning the Cohen-Macaulay property of invariants of Hopf algebras. Tony Geramita asked me to write up my notes for the Queen’s Papers, and I happily took up his suggestion. Although this article focuses on the proof of one main theorem (Theorem 2.11 on page 12), it has some of the character of ...