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S L 2 , the cubic and the quartic

Yannis Y. Papageorgiou (1998)

Annales de l'institut Fourier

We describe the branching rule from S p 4 to S L 2 , where the latter is embedded via its action on binary cubic forms. We obtain both a numerical multiplicity formula, as well as a minimal system of generators for the geometric realization of the rule.

Semi n -ideals of commutative rings

Ece Yetkin Çelikel, Hani A. Khashan (2022)

Czechoslovak Mathematical Journal

Let R be a commutative ring with identity. A proper ideal I is said to be an n -ideal of R if for a , b ∈ R , a b ∈ I and a ∉ 0 imply b ∈ I . We give a new generalization of the concept of n -ideals by defining a proper ideal I of R to be a semi n -ideal if whenever a ∈ R is such that a 2 ∈ I , then a ∈ 0 or a ∈ I . We give some examples of semi n -ideal and investigate semi n -ideals under various contexts of constructions such as direct products, homomorphic images and localizations. We present various characterizations of this new class of...

Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids

Víctor Blanco, Pedro A. García-Sánchez, Alfred Geroldinger (2010)

Actes des rencontres du CIRM

Arithmetical invariants—such as sets of lengths, catenary and tame degrees—describe the non-uniqueness of factorizations in atomic monoids.We study these arithmetical invariants by the monoid of relations and by presentations of the involved monoids. The abstract results will be applied to numerical monoids and to Krull monoids.

Separating ideals in dimension 2.

James J. Madden, Niels Schwartz (1997)

Revista Matemática de la Universidad Complutense de Madrid

Experience shows that in geometric situations the separating ideal associated with two orderings of a ring measures the degree of tangency of the corresponding ultrafilters of semialgebraic sets. A related notion of separating ideals is introduced for pairs of valuations of a ring. The comparison of both types of separating ideals helps to understand how a point on a surface is approached by different half-branches of curves.

Sequences between d-sequences and sequences of linear type

Hamid Kulosman (2009)

Commentationes Mathematicae Universitatis Carolinae

The notion of a d-sequence in Commutative Algebra was introduced by Craig Huneke, while the notion of a sequence of linear type was introduced by Douglas Costa. Both types of sequences generate ideals of linear type. In this paper we study another type of sequences, that we call c-sequences. They also generate ideals of linear type. We show that c-sequences are in between d-sequences and sequences of linear type and that the initial subsequences of c-sequences are c-sequences. Finally we prove a...

Solution d'une conjecture de C. Berenstein - A. Yger et invariants de contact à l'infini

Michel Hickel (2001)

Annales de l’institut Fourier

Soient k un corps commutatif et I = ( p 1 , ⋯ , p m ) k n [ X ] un idéal de l’anneau des polynômes k [ X 1 , ⋯ , X n ] (éventuellement I = k n [ X ] ). Nous prouvons une conjecture de C. Berenstein - A. Yger qui affirme que pour tout polynôme p , élément de la clôture intégrale I ¯ de l’idéal I , on a une représentation p m = ∑ 1 ≤ i ≤ m p i q i , avec max deg ( q i p i ) ≤ m deg p + m d 1 ⋯ d m , où d i = deg p i , 1 ≤ i ≤ m .

Currently displaying 461 – 480 of 651