Dérivées et différences divisées à valeurs entières
Dimension des couples d'anneaux partageant un idéal
Dubrovnic, Valuation Rings and Henselization.
Extensions de valuation et polygone de Newton
Soient un corps valué et est une extension monogène finie de définie par , alors toute valuation de qui prolonge définit une pseudo-valuation de de noyau l’idéal . Nous savons associer à une famille de valuations de , appelée famille admissible, construite de façon explicite à partir de valuations augmentées et de valuations augmentées limites.Nous donnons une condition nécessaire et suffisante pour qu’une valuation de appartienne à la famille admissible associée à une pseudo-valuation...
Formal prime ideals of infinite value and their algebraic resolution
Suppose that is a local domain essentially of finite type over a field of characteristic , and a valuation of the quotient field of which dominates . The rank of such a valuation often increases upon extending the valuation to a valuation dominating , the completion of . When the rank of is , Cutkosky and Ghezzi handle this phenomenon by resolving the prime ideal of infinite value, but give an example showing that when the rank is greater than , there is no natural ideal in that...
-domains and pseudo-valuations
Inegalite relative des genres.
Konstantenreduktion von Ringen und Moduln.
Local monomialization of transcendental extensions
Suppose that are regular local rings which are essentially of finite type over a field of characteristic zero. If is a valuation ring of the quotient field of which dominates , then we show that there are sequences of monoidal transforms (blow ups of regular primes) and along such that is a monomial mapping. It follows that a morphism of nonsingular varieties can be made to be a monomial mapping along a valuation, after blow ups of nonsingular subvarieties.
Manis valuations and Prüfer extensions
Manis valuations and Prüfer extensions. I.
Maximal non -subrings
Let be a commutative ring with unity. The notion of maximal non -subrings is introduced and studied. A ring is called a maximal non -subring of a ring if is not a -extension, and for any ring such that , is a -extension. We show that a maximal non -subring of a field has at most two maximal ideals, and exactly two if is integrally closed in the given field. A determination of when the classical construction is a maximal non -domain is given. A necessary condition is given...
Maximal non-Jaffard subrings of a field.
A domain R is called a maximal non-Jaffard subring of a field L if R ⊂ L, R is not a Jaffard domain and each domain T such that R ⊂ T ⊆ L is Jaffard. We show that maximal non-Jaffard subrings R of a field L are the integrally closed pseudo-valuation domains satisfying dimv R = dim R + 1. Further characterizations are given. Maximal non-universally catenarian subrings of their quotient fields are also studied. It is proved that this class of domains coincides with the previous class when R is integrally...
Nash Wings and Real Prime Divisors.
Noncommutative Valuation Rings
Notes on structure of complete discrete valuation rings.
On a generalization of a Prüfer-Kaplansky-Procházka theorem
On chains of centered valuations.
On chains of free modules over valuation domains
On -rings that are not formally real
Henriksen and Isbell showed in 1962 that some commutative rings admit total orderings that violate equational laws (in the language of lattice-ordered rings) that are satisfied by all totally-ordered fields. In this paper, we review the work of Henriksen and Isbell on this topic, construct and classify some examples that illustrate this phenomenon using the valuation theory of Hion (in the process, answering a question posed in [E]) and, finally, prove that a base for the equational theory of totally-ordered...