Valuation rings and the (catenary) chain conjectures
نویسندگان
چکیده
منابع مشابه
Pseudo-almost valuation rings
The aim of this paper is to generalize thenotion of pseudo-almost valuation domains to arbitrary commutative rings. It is shown that the classes of chained rings and pseudo-valuation rings are properly contained in the class of pseudo-almost valuation rings; also the class of pseudo-almost valuation rings is properly contained in the class of quasi-local rings with linearly ordere...
متن کاملAlmost valuation rings
The aim of this paper is to generalize the notion of almost valuation domains to arbitrary commutative rings. Also, we consider relations between almost valuation rings and pseudo-almost valuation rings. We prove that the class of almost valuation rings is properly contained in the class of pseudo-almost valuation rings. Among the properties of almost valuation rings, we sh...
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Classical Buchberger theory is generalized to a new family of rings. The family includes all subalgebras of the polynomial algebra in one variable. Some subalgebras of polynomial algebras in several variables are included. The new rings are integral domains and have a number of other properties in common with polynomial rings. The rings sit in a field F in appropriate position relative to a val...
متن کاملReal closed valuation rings
The real closed valuation rings, i.e., convex subrings of real closed fields, form a proper subclass of the class of real closed domains. It is shown how one can recognize whether a real closed domain is a valuation ring. This leads to a characterization of the totally ordered domains whose real closure is a valuation ring. Real closures of totally ordered factor rings of coordinate rings of re...
متن کاملComplete fields and valuation rings
In order to make further progress in our investigation of finite extensions L/K of the fraction field K of a Dedekind domain A, and in particular, to determine the primes p of K that ramify in L, we introduce a new tool that allows us to “localize” fields. We have seen how useful it can be to localize the ring A at a prime ideal p: this yields a discrete valuation ring Ap, a principal ideal dom...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1978
ISSN: 0021-8693
DOI: 10.1016/0021-8693(78)90264-8