LCM-Stability of Power Series Extensions Characterizes Dedekind Domains

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.