LCM-Stability of Power Series Extensions Characterizes Dedekind Domains

Author

John T. Condo, University of Tennessee - Knoxville

Date of Award

5-1991

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

David E. Dobbs

Committee Members

Robert McConnel, David Anerson, Thomas Handle

Abstract

In this dissertation, we prove the following main result in Chapter 3. A (communicative integral) domain R is a Dedekind domain if and only if R[[X]] ⊂ T[[X]] is LCM-stable of each domain T containing R as a subring. Analogous results on flatness are given in Chapter 4. Complete statements of results cited from the literature appear in Chapter 2, while Chapter 1 places the above stated main result in historical context, as extending work of F. Richman and H. Uda.

Recommended Citation

Condo, John T., "LCM-Stability of Power Series Extensions Characterizes Dedekind Domains. " PhD diss., University of Tennessee, 1991.
https://trace.tennessee.edu/utk_graddiss/2927