Prime ideals in low-dimensional mixed polynomial/power series rings

Abstract

Let B be a simple birational extension of R[[x]], the ring of power series in one variable over a one-dimensional Noetherian domain R. We consider Spec( B), the set of prime ideals of B partially ordered by inclusion. The main result of Chapter 2 is a characterization of Spec( B), where R is a countable PID or an order in an algebraic number field. Among other results in Chapter 3 is a characterization of Spec(R[[x]][y]/ Q) for certain height-one prime ideals Q in R [[x]][y], where R is a countable semilocal one-dimensional Noetherian domain. In Chapter 4 we give some properties of prime spectra of certain three-dimensional mixed polynomial/power series rings.