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arXiv · 2009.03042

Maximal non valuative domains

Rahul Kumar·Atul Gaur
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Abstract

The notion of maximal non valuative domain is introduced and characterized. An integral domain R is called a maximal non valuative domain if R is not a valuative domain but every proper overring of R is a valuative domain. Maximal non valuative domains have at most four maximal ideals. Various properties of maximal non valuative domains are discussed. Conditions are given under which pseudo-valuation domains and maximal non pseudo-valuation domains are maximal non valuative domains.

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Rahul Kumar, Atul Gaur. 2020-09-07. Maximal non valuative domains. https://arxiv.org/abs/2009.03042

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