We investigate the Cohen-Macaulay property for rings of invariants under multiplicative actions of a finite group G. By definition, these are G-actions on Laurent polynomial algebras k[x 1 , . . . , x ±1 n ] that stabilize the multiplicative group consisting of all monomials in the variables xi. For the most part, we concentrate on the case where the base ring k is Z. Our main result states tha...

This paper studies Frobenius powers of parameter ideals in a commutative Noetherian local ring R of prime characteristic p. For a given ideal a of R, there is a power Q of p, depending on a, such that the Q-th Frobenius power of the Frobenius closure of a is equal to the Q-th Frobenius power of a. The paper addresses the question as to whether there exists a uniform Q0 which ‘works’ in this con...

We investigate Sharifan and Moradi’s closed neighborhood ideal of a finite simple graph, which is square-free monomial in polynomial ring over field. explicitly describe the minimal irreducible decompositions these ideals. also characterize trees whose ideals are Cohen–Macaulay; particular, this property for characteristic independent.

Various classification theorems of thick subcategories of a triangulated category have been obtained in many areas of mathematics. In this paper, as a higher dimensional version of the classification theorem of thick subcategories of the stable category of finitely generated representations of a finite p-group due to Benson, Carlson and Rickard, we consider classifying thick subcategories of th...

The notion of the Cousin complex of a module was given by Sharp in 1969. It wasn’t known whether its cohomologies are finitely generated until recently. In 2001, Dibaei and Tousi showed that the Cousin cohomologies of a finitely generated A-module M are finitely generated if the base ring A is local, has a dualizing complex, M satisfies Serre’s (S2)-condition and is equidimensional. In the pres...

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.