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Griffith, Phillip A. Smith, Daniel Aaron 2015-09-28T15:20:27Z 2015-09-28T15:20:27Z 10000-01-01 1999 1999 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. Made available in DSpace on 2015-09-28T15:20:27Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9945003.pdf: 1183412 bytes, checksum: e0aee14a72465fd3b53484117ccc013f (MD5) Previous issue date: 1999 Embargo set by: Seth Robbins for item 88261 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 24 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1999. http://hdl.handle.net/2142/86980 (MiAaPQ)AAI9945003 eng Mathematics A Variation on a Theme of Vasconcelos text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.