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Alexander and Hirschowitz determined the Hilbert function of a generic union of fat points in a projective space when the number of fat points is much bigger than the greatest multiplicity of the fat points. Their method is based on a lemma which determines the limit of a linear system depending on fat points approaching a divisor.Other Hilbert functions were computed previously by Nagata. In connection with his counter-example to Hilbert’s fourteenth problem, Nagata determined the Hilbert function...
We develop a recursive method for computing the -removed -orderings and -orderings of order the characteristic sequences associated to these and limits associated to these sequences for subsets of a Dedekind domain This method is applied to compute these objects for and .
First, we give complete description of the comultiplication modules over a Dedekind domain. Second, if is the pullback of two local Dedekind domains, then we classify all indecomposable comultiplication -modules and establish a connection between the comultiplication modules and the pure-injective modules over such domains.
All rings considered in this paper are assumed to be commutative with identities. A ring is a -ring if every ideal of is a finite product of primary ideals. An almost -ring is a ring whose localization at every prime ideal is a -ring. In this paper, we first prove that the statements, is an almost -ring and is an almost -ring are equivalent for any ring . Then we prove that under the condition that every prime ideal of is an extension of a prime ideal of , the ring is a (an almost)...
Une somme amalgamée de schémas est décrite localement par un produit fibré d’anneaux. Ce texte donne un résultat global d’existence (§5.4) de schémas définis comme certaines sommes amalgamées et un procédé algébrique (§2.2) pour décrire les modules sur produits fibrés d’anneaux correspondants.
A ternary ring is an algebraic structure of type satisfying the identities and where, moreover, for any , , there exists a unique with . A congruence on is called normal if is a ternary ring again. We describe basic properties of the lattice of all normal congruences on and establish connections between ideals (introduced earlier by the third author) and congruence kernels.
Let be the algebraic closure of and be the local field of formal power series with coefficients in . The aim of this paper is the description of the set of conjugacy classes of series of order for the composition law. This work is concerned with the formal power series with coefficients in a field of characteristic which are invertible and of finite order for the composition law. In order to investigate Oort’s conjecture, I give a description of conjugacy classes of series by means...
Gröbner bases for modules are used to calculate a generalized linear immersion for a plant whose solutions to its regulation equations are polynomials or pseudo-polynomials. After calculating the generalized linear immersion, we build the controller which gives the robust regulation.
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