Thesis Title

Bourbaki Ideals

Date of Graduation

Summer 2008

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Mark Rogers

Keywords

Bourbaki ideals, Bourbaki's theorem, modules, rank, ideals, torsion

Subject Categories

Mathematics

Abstract

Bourbaki's theorem states that if M is a finitely generated torsion free module of rank n over a Noetherian integrally closed domain R, then M has a free submodule F of rank n -1 such that the quotient M/F is isomorphic to an ideal of R. In this paper we examine the theory of modules used in exploring Bourbaki ideals, and we prove various theorems which are useful in the proof of Bourbaki's Theorem. We prove that for any ideal of a Noetherian integral domain there is a module of any given rank having that ideal as a Bourbaki ideal. Finally we compute several examples of Bourbaki ideals for specfic modules over polynomial rings with rational coefficients.

Copyright

© Carrie A. Whittle

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