Graded rings associated with contracted ideals

Graded Rings Associated with Contracted Ideals

The study of the ideals in a regular local ring (R,m) of dimension 2 has a long and important tradition dating back to the fundamental work of Zariski [ZS]. More recent contributions are due to several authors including Cutkosky, Huneke, Lipman, Sally and Tessier among others, see [C1, C2, H, HS, L, LT]. One of the main result in this setting is the unique factorization theorem for complete (i....

On Associated Graded Rings of Normal Ideals

Normal Ideals of Graded Rings

For a graded domain R = k[X0, ...,Xm]/J over an arbitrary domain k, it is shown that the ideal generated by elements of degree ≥ mA, where A is the least common multiple of the weights of the Xi, is a normal ideal.

Depth of Associated Graded Rings via Hilbert Coefficients of Ideals

Given a local Cohen-Macaulay ring (R,m), we study the interplay between the integral closedness – or even the normality – of an m-primary R-ideal I and conditions on the Hilbert coefficients of I . We relate these properties to the depth of the associated graded ring of I .

Ideals Whose Associated Graded Rings Are Isomorphic to the Base Rings

Let k be a field. We determine the ideals I in a finitely generated graded k-algebra A, whose associated graded rings ⊕ n≥0 I/I are isomorphic to A. Also we compute the graded local cohomologies of the Rees rings A[It] and give the condition for A[It] to be generalized Cohen-Macaulay under the condition that A is generalized Cohen-Macaulay. MSC: 13A30, 13D45 Introduction Let k be a field and S ...