We study properties of a poset generating a Cohen-Macaulay algebra with straightening laws (ASL for short). We show that if a poset P generates a Cohen-Macaulay ASL, then P is pure and, if P is moreover Buchsbaum, then P is Cohen-Macaulay. Some results concerning a Rees algebra of an ASL defined by a straightening closed ideal are also established. And it is shown that if P is a Cohen-Macaulay ...

A commutative local Cohen-Macaulay ring R of finite Cohen-Macaulay type is known to be an isolated singularity; that is, Spec(R) \ {m} is smooth. This paper proves a non-commutative analogue. Namely, if A is a (non-commutative) graded Artin-Schelter Cohen-Macaulay algebra which is FBN and has finite Cohen-Macaulay type, then the non-commutative projective scheme determined by A is smooth.

Shellability is a well-known combinatorial criterion on a simplicial complex ∆ for verifying that the associated Stanley-Reisner ring k[∆] is Cohen-Macaulay. A notion familiar to commutative algebraists, but which has not received as much attention from combinatorialists as the Cohen-Macaulay property, is the notion of a Golod ring. Recently, Jöllenbeck introduced a criterion on simplicial comp...

For a partition λ of n ∈ N , let I Sp be the ideal R = K [ x 1 … ] generated by all Specht polynomials shape . In previous paper, second author showed that if / is Cohen-Macaulay, then either ( − d ) or and converse true char 0 this we compute Hilbert series for Hence, get Castelnuovo-Mumford regularity when it Cohen-Macaulay. particular, has + 2 -linear resolution in Cohen–Macaulay case.

In this article, we delve into the properties possessed by algebras, which we have termed seeds, that map to big Cohen-Macaulay algebras. We will show that over a complete local domain of positive characteristic any two big Cohen-Macaulay algebras map to a common big Cohen-Macaulay algebra. We will also strengthen Hochster and Huneke’s “weakly functorial” existence result for big Cohen-Macaulay...