Date of Award
Doctor of Philosophy
David E. Dobbs
Robert McConnel, David Anerson, Thomas Handle
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.
Condo, John T., "LCM-Stability of Power Series Extensions Characterizes Dedekind Domains. " PhD diss., University of Tennessee, 1991.