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

Christina Eubanks-Turner, University of Nebraska - Lincoln


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. ^

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Recommended Citation

Eubanks-Turner, Christina, "Prime ideals in low-dimensional mixed polynomial/power series rings" (2008). ETD collection for University of Nebraska - Lincoln. AAI3303652.