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Description
Title: | A Variation on a Theme of Vasconcelos |
Author(s): | Smith, Daniel Aaron |
Doctoral Committee Chair(s): | Griffith, Phillip A. |
Department / Program: | Mathematics |
Discipline: | Mathematics |
Degree Granting Institution: | University of Illinois at Urbana-Champaign |
Degree: | Ph.D. |
Genre: | Dissertation |
Subject(s): | Mathematics |
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 |
Type: | Text |
Language: | English |
Description: | 24 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1999. |
URI: | http://hdl.handle.net/2142/86980 |
Other Identifier(s): | (MiAaPQ)AAI9945003 |
Date Available in IDEALS: | 2015-09-28 |
Date Deposited: | 1999 |
This item appears in the following Collection(s)
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Dissertations and Theses - Mathematics
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Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois