Let KV ] G be the invariant ring of a nite linear group G GL(V), and let GU be the pointwise stabilizer of a subspace U V. We prove that the following numbers associated to the invariant ring decrease if one passes from KV ] G to KV ] G U : the minimal number of homogeneous generators, the maximal degree of the generators, the number of syzygies and other Betti numbers, the complete intersectio...

Let K[V ] be the invariant ring of a finite linear group G ≤ GL(V ), and let GU be the pointwise stabilizer of a subspace U ≤ V . We prove that the following numbers associated to the invariant ring do not increase if one passes from K[V ] to K[V ]U : the minimal number of homogeneous generators, the maximal degree of the generators, the number of syzygies and other Betti numbers, the complete ...

In the late 1960s Auslander and Bridger [2] introduced a notion of approximation which they used to prove that every module whose n syzygy is n-torsionfree can be described as the quotient of an n-spherical module by a submodule of projective dimension less than n. About two decades later Auslander and Buchweitz [3] introduced the notion of Cohen-Macaulay approximation which they used to show t...

In a local Cohen-Macaulay ring (A, m), we study the Hilbert function of an m-primary ideal I whose reduction number is two. It continuous work papers Huneke, Ooishi, Sally, and Goto-Nishida-Ozeki. With some conditions, show inequality e1(I) ? e0(I) ? ?A(A/I) + e2(I) coefficients, which converse Sally Itoh. We also relations between coefficients depth associated graded ring.

We study the quotient complex ∆(B lm)/S l ≀ Sm as a means of deducing facts about the ring k[x 1 ,. .. , x lm ] S l ≀Sm. It is shown in [He] that ∆(B lm)/S l ≀ Sm is shellable when l = 2, implying Cohen-Macaulayness of k[x 1 ,. .. , x 2m ] S 2 ≀Sm for any field k. We now confirm for all pairs (l, m) with l > 2 and m > 1 that ∆(B lm)/S l ≀ Sm is not Cohen-Macaulay over Z Z/2Z Z, but it is Cohen-...

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 .

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.