Abstract
In [2] Eisenbud and Evans gave an important generalization of Krullâs Principal Ideal Theorem. However, their proof, using maximal Cohen-Macaulay modules, may have limited the validity of their theorem to a proper subclass of all local rings. (Hochster proved the existence of maximal Cohen-Macaulay modules for local rings which contain a field, cf. [4]). In the first section we present a proof which is simpler and guarantees the Generalized Principal Ideal Theorem for all local rings. The main result of the second section was conjectured in [2]. Under a hypothesis typically being satisfied for the most important fitting invariant of a module, it improves the Eagon-Northcott bound [1] on the height of a determinantai ideal considerably. Finally we will discuss the implications of a recent theorem of Fairings [3] on determinantal ideals.
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.
