A Variation on a Theme of Vasconcelos

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 &le; 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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Smith, Daniel Aaron

Contributors dc:contributor

• Griffith, Phillip A.

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI9945003

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86980