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Title:A Variation on a Theme of Vasconcelos
Author(s):Smith, Daniel Aaron
Doctoral Committee Chair(s):Griffith, Phillip A.
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Abstract:In 1967, Vasconcelos and Ferrand independently demonstrated that an ideal I in a Noetherian local ring R is generated by a regular sequence if and only if I/ I2 is free over R/I and pdRI < infinity. In this thesis, we prove that a radical ideal I in an excellent local normal domain is generated by a regular sequence provided R/I satisfies the Serre condition S2, I/ I(2) is R/I-free, and I is generated by a regular sequence when localized at primes P containing I such that hat P/I ≤ 1. In particular, we are able to replace the strong assumption pdRI < infinity with essentially weaker hypotheses. Our proof makes use of lifting as presented by Auslander, Ding and Slobbered [1993] together with a finer analysis of the elimination of the obstructions to lifting cyclic modules. Subsequently, we develop some criteria for lifting a module M in a more general setting. Our approach here is to again assume the conclusion holds when localizing at primes of low codimension while also requiring M and a related module of morphemes to possess sufficient depth in the remaining cases.
Issue Date:1999
Description:24 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1999.
Other Identifier(s):(MiAaPQ)AAI9945003
Date Available in IDEALS:2015-09-28
Date Deposited:1999

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