Abstract
In this paper, we address the following question: for a nonzero finitely generated ideal [Formula: see text] of a multivariate polynomial ring [Formula: see text] over a coherent ring [Formula: see text], fixing a monomial order [Formula: see text] on [Formula: see text], is the trailing terms ideal [Formula: see text] of [Formula: see text] (that is, the ideal generated by the trailing terms of the nonzero polynomials in [Formula: see text]) finitely generated? We show that while [Formula: see text] can be nonfinitely generated, it is always countably generated when the monomial order is Noetherian (graded monomial orders as instances).
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.
