Abstract
We establish several new characterizations of maximal non-valuation subrings of a field involving several concepts of commutative algebra related to the set of prime ideals and the set of overrings. For example we show that an integral domain R of finite dimension d is a maximal non-valuation subring of a field if, and only if R is either integrally closed with a set of overrings isomorphic to a kite-graph of dimension d + 1, or is non-integrally closed with a chained set of overrings of dimension d + 1.
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Schedule a callMore From: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
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