Uniform Properties of Ideals in Rings of Restricted Power Series

Abstract When is an ideal of a ring radical or prime? By examining its generators, one may in many cases definably and uniformly test the ideal’s properties. We seek to establish such definable formulas rings p -adic power series, as $\mathbb Q_{p}\langle X\rangle $ , Z_{p}\langle related series over more general valuation their fraction fields. obtain definable, uniform for radicality, and, one-dimensional case, primality. This builds upon techniques stemming from proof quantifier elimination results analytic theory integers by Denef van den Dries, linear algebra methods Hermann Seidenberg. prepared Madeline G. Barnicle. E-mail : [email protected] URL https://escholarship.org/uc/item/6t02q9s4