We investigate monomial labellings on cell complexes, giving a minimal cellular resolution of the ideal generated by these monomials, and such that the associated quotient ring is Cohen-Macaulay. We introduce a notion of such a labelling being maximal. There is only a finite number of maximal labellings for each cell complex, and we classify these for trees, partly for subdivisions of polygons,...

We show the existence of a first order theory Cmd,e whose Noetherian models are precisely the local Cohen-Macaulay rings of dimension d and multiplicity e. The completion of a model of Cmd,e is again a model and is moreover Noetherian. If R is an equicharacteristic local Gorenstein ring of dimension d and multiplicity e with algebraically closed residue field and if the Artin Approximation Prop...

The concept of a combinatorial decomposition of a graded K algebra was introduced by Baclawski-Garsia [4], and they showed that every (finitelygenerated) graded K algebra has such a decomposition. The purpose of this paper is to prove some general properties of combinatorial decompositions, which are useful for finding such decompositions. We then show how to compute combinatorial decomposition...

This paper considers the problems of finite determinacy and approximation flat analytic maps from germs real (resp. complex) spaces to R </mml...

We study rings of integral modular forms for congruence subgroups as modules over the ring full group. In many cases these are free or decompose at least into well-understood pieces. apply this to characterize which Cohen--Macaulay and prove finite generation results. These theorems based on decomposition results about vector bundles compactified moduli stack elliptic curves.

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.

Given a local Noetherian ring (R, m) of dimension d > 0 and infinite residue field, we study the invariants (dimension and multiplicity) of the Sally module SJ (I) of any m-primary ideal I with respect to a minimal reduction J. As a by-product we obtain an estimate for the Hilbert coefficients of m that generalizes a bound established by J. Elias and G. Valla in a local Cohen-Macaulay setting. ...

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...

In this article, we introduce an invariant of Cohen-Macaulay local rings in terms the reduction number canonical ideals. The can be defined arbitrary and it measures how close to being Gorenstein. First, clarify relation between almost Gorenstein nearly by using dimension one. We next characterize idealization trace ideals over invariant. It provides better prospects for a result on property id...