Abstract
We study the ring of integral valued polynomials over a pseudovaluation domain A. We entirely determine the set of prime ideals above the maximal ideal M of A: if M is a principal ideal in the valuation domain V associated with A and if its residue field is finite, then this set is in bijection with a topologically complete ring, as in the Noetherian case; if M is principal but of infinite residue field in V, then this set is finite; at last, if M is not principal, then the ring of integral valued polynomials is included in V[X] and has the same set of prime ideals above M.
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Cahen, PJ., Haouat, Y. Polynomes a valeurs entieres sur un anneau de pseudovaluation. Manuscripta Math 61, 23–31 (1988). https://doi.org/10.1007/BF01153579
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DOI: https://doi.org/10.1007/BF01153579