Abstract
Let [Formula: see text] be a regular ideal in noetherian ring [Formula: see text]. Mc Adam and Ratliff showed the existence of the unique minimal reduction number of [Formula: see text], noted [Formula: see text], such that for every minimal reduction [Formula: see text] of [Formula: see text], [Formula: see text] and [Formula: see text]. They showed that the set of integers [Formula: see text] is bounded in terms of the analytic spread of [Formula: see text]. Here, we extend these results to good filtrations. Let [Formula: see text] be a good filtration on [Formula: see text], we show that the set of integers [Formula: see text] is bounded.
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.
