Invariants of Cohen–Macaulay rings associated to their canonical ideals

Associated Prime Ideals of Skew Polynomial Rings

In this paper, it has been proved that for a Noetherian ring R and an automorphism σ of R, an associated prime ideal of R[x, σ] or R[x, x−1, σ] is the extension of its contraction to R and this contraction is the intersection of the orbit under σ of some associated prime ideal of R. The same statement is true for minimal prime ideals also. It has also been proved that for a Noetherian Q-algebra...

On Associated Graded Rings of Normal 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....

Separative Ideals of Exchange Rings

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 ...