Abstract
We show that, an integrally closed domain, such that each of its overrings is treed (or going-down) is locally pseudo-valuation (so going-down). This result provides a general answer to a question of Dobbs (Rend Math 7:317–322, 1987).
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The author thanks the referee for his several helpful remarks concerning the final form of this paper.
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Communicated by Marco Fontana.
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Ayache, A. Integrally closed domains with treed overrings. Ricerche mat. 63, 93–100 (2014). https://doi.org/10.1007/s11587-013-0166-4
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DOI: https://doi.org/10.1007/s11587-013-0166-4