English

Maximal non valuative domains

Commutative Algebra 2020-09-08 v1

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.

Cite

@article{arxiv.2009.03042,
  title  = {Maximal non valuative domains},
  author = {Rahul Kumar and Atul Gaur},
  journal= {arXiv preprint arXiv:2009.03042},
  year   = {2020}
}
R2 v1 2026-06-23T18:21:31.138Z