Abstract
For an integral domain D of dimension n, the dimension of the polynomial ring D[ x ] is known to be bounded by n + 1 and 2n + 1. While n + 1 is a lower bound for the dimension of the power series ring D[[ x ]], it often happens that D[[ x ]] has infinite chains of primes. For example, such chains exist if D is either an almost Dedekind domain that is not Dedekind or a one-dimensional nondiscrete valuation domain. The main concern here is in developing a scheme by which such chains can be constructed in the gap between MV[[ x ]] and M[[ x ]] when V is a one-dimensional nondiscrete valuation domain with maximal ideal M. A consequence of these constructions is that there are chains of primes similar to the set of ω1 transfinite sequences of 0's and 1's ordered lexicographically.
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