Date of Graduation
Master of Science in Mathematics
Bourbaki ideals, Bourbaki's theorem, modules, rank, ideals, torsion
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.
© Carrie A. Whittle
Whittle, Carrie A., "Bourbaki Ideals" (2008). MSU Graduate Theses. 1629.