Prime T-Ideals in Polynomial and Power Series Rings Over a Pseudo-Valuation Domain

Let R be an m-dimensional pseudo-valuation domain with residue field k, let V be the associated valuation domain with residue field K, and let k ₀ be the maximal separable extension of k in K. We compute the t-dimension of polynomial and power series rings over R. It is easy to see that t-dim Rx ₁,…, x _n ] = 2 if m = 1 and K is transcendental over k, but equals m otherwise, and that t-dim Rx ₁,…, x _n ]] = ∞ if R is a nonSFT-ring. When R is an SFT-ring, we also show that: (1) t-dim Rx]] = m; (2) t-dim Rx ₁,…, x _n ]] = 2m ? 1, if n ≥ 2, K has finite exponent over k ₀, and k ₀: k] < ∞; (3) t-dim Rx ₁,…, x _n ]] = 2m, otherwise.