Abstract
We provide a large class of coherent domains whose rings of formal power series are not coherent, by proving that if R is a pseudo-Bezout domain and R[[ X]] is coherent, then R is completely integrally closed; this generalizes a theorem of Jøndrup and Small's for valuation domains. We also obtain a large class of completely integrally closed pseudo-Bezout domains R for which R[[ X]] is not coherent; in particular, if R is a rank one valuation domain whose group of divisibility is a proper dense subgroup of the reals, then R[[ X]] is not coherent.
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