Abstract
We establish a bound for the Castelnuovo–Mumford regularity of the associated graded ring GI(A) of an m-primary ideal I of a local Noetherian ring (A,m) in terms of the dimension of A, the relation type and the number of generators of I. As a consequence, we obtain that the existence of uniform bounds for the regularity of the associated graded ring, and the relation type of parameter ideals in A, are equivalent conditions. In addition, we establish an equation for the postulation number and the Castelnuovo–Mumford regularity of the associated graded ring Gq(A) of a parameter ideal q, which holds under certain conditions on the depths of the occurring rings. We also show, that the regularity of the ring Gq(A) is bounded in terms of the dimension of A, the length of A/q and the postulation number of Gq(A).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
