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Border bases and kernels of homomorphisms and of derivations

Janusz Zieliński (2010)

Open Mathematics

Border bases are an alternative to Gröbner bases. The former have several more desirable properties. In this paper some constructions and operations on border bases are presented. Namely; the case of a restriction of an ideal to a polynomial ring (in a smaller number of variables), the case of the intersection of two ideals, and the case of the kernel of a homomorphism of polynomial rings. These constructions are applied to the ideal of relations and to factorizable derivations.

Bornes pour la régularité de Castelnuovo-Mumford des schémas non lisses

Amadou Lamine Fall (2009)

Annales de l’institut Fourier

Nous montrons dans cet article des bornes pour la régularité de Castelnuovo-Mumford d’un schéma admettant des singularités, en fonction des degrés des équations définissant le schéma, de sa dimension et de la dimension de son lieu singulier. Dans le cas où les singularités sont isolées, nous améliorons la borne fournie par Chardin et Ulrich et dans le cas général, nous établissons une borne doublement exponentielle en la dimension du lieu singulier.

Boundary map and overrings of half-factorial domains

Nathalie Gonzalez, Sébastien Pellerin (2005)

Bollettino dell'Unione Matematica Italiana

We investigate factorization of elements in overrings of a half-factorial domain A in relation with the behaviour of the boundary map of A . It turns out that a condition, called C ⋆ , on the extension plays a central role in this study. We finally apply our results to the special case of A + X ⁢ B ⁢ X polynomial rings.

Bounds for quotients in rings of formal power series with growth constraints

Vincent Thilliez (2002)

Studia Mathematica

In rings Γ M of formal power series in several variables whose growth of coefficients is controlled by a suitable sequence M = ( M l ) l ≥ 0 (such as rings of Gevrey series), we find precise estimates for quotients F/Φ, where F and Φ are series in Γ M such that F is divisible by Φ in the usual ring of all power series. We give first a simple proof of the fact that F/Φ belongs also to Γ M , provided Γ M is stable under derivation. By a further development of the method, we obtain the main result of the paper, stating that...

Bounds on Bass numbers and their dual

Abolfazl Tehranian, Siamak Yassemi (2007)

Archivum Mathematicum

Let ( R , 𝔪 ) be a commutative Noetherian local ring. We establish some bounds for the sequence of Bass numbers and their dual for a finitely generated R -module.

Bounds on Castelnuovo-Mumford regularity for divisors on rational normal scrolls.

Chikashi Miyazaki (2005)

Collectanea Mathematica

The Castelnuovo-Mumford regularity is one of the most important invariants in studying the minimal free resolution of the defining ideals of the projective varieties. There are some bounds on the Castelnuovo-Mumford regularity of the projective variety in terms of the other basic invariants such as dimension, codimension and degree. This paper studies a bound on the regularity conjectured by Hoa, and shows this bound and extremal examples in the case of divisors on rational normal scrolls.

Bounds on multisecant lines.

Scott Nollet (1998)

Collectanea Mathematica

The purpose of this paper is twofold. First, we give an upper bound on the order of a multisecant line to an integral arithmetically Cohen-Macaulay subscheme in Pn of codimension two in terms of the Hilbert function. Secondly, we give an explicit description of the singular locus of the blow up of an arbitrary local ring at a complete intersection ideal. This description is used to refine a standard linking theorem. These results are tied together by the construction of sharp examples for the bound,...

C -Gorenstein projective, injective and flat modules

Xiao Yan Yang, Zhong Kui Liu (2010)

Czechoslovak Mathematical Journal

By analogy with the projective, injective and flat modules, in this paper we study some properties of C -Gorenstein projective, injective and flat modules and discuss some connections between C -Gorenstein injective and C -Gorenstein flat modules. We also investigate some connections between C -Gorenstein projective, injective and flat modules of change of rings.

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