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.