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Note sur un article de Sharif et Woodcock

Jean-Paul Allouche (1989)

Journal de théorie des nombres de Bordeaux

H. Sharif et C. Woodcock donnent dans [26] une caractérisation des séries formelles à coefficients dans un corps K de caractéristique non nulle et algébriques sur K ( X ) ; ils en déduisent simplement l’algébricité du produit de Hadamard ou des diagonales de séries algébriques. (Ces résultats ont aussi été obtenus par T. Harase [14]). Nous donnons ici une démonstration légèrement différente de leur théorème et montrons comment on peut en déduire une généralisation intéressante de la notion de p k -substitution...

Notes on generalizations of Bézout rings

Haitham El Alaoui, Hakima Mouanis (2021)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we give new characterizations of the P - 2 -Bézout property of trivial ring extensions. Also, we investigate the transfer of this property to homomorphic images and to finite direct products. Our results generate original examples which enrich the current literature with new examples of non- 2 -Bézout P - 2 -Bézout rings and examples of non- P -Bézout P - 2 -Bézout rings.

Numerical characters of graded algebras

Giuseppe Valla (2004)

Bollettino dell'Unione Matematica Italiana

This is the summary of the plenary talk I gave in Milan at the XVII Meeting of the Unione Matematica Italiana. We focus on some relevant numerical characters of the standard graded algebras and, in some case, we explain their geometric meaning.

Numerical semigroups with a monotonic Apéry set

José Carlos Rosales, Pedro A. García-Sánchez, Juan Ignacio García-García, M. B. Branco (2005)

Czechoslovak Mathematical Journal

We study numerical semigroups S with the property that if m is the multiplicity of S and w ( i ) is the least element of S congruent with i modulo m , then 0 < w ( 1 ) < ⋯ < w ( m - 1 ) . The set of numerical semigroups with this property and fixed multiplicity is bijective with an affine semigroup and consequently it can be described by a finite set of parameters. Invariants like the gender, type, embedding dimension and Frobenius number are computed for several families of this kind of numerical semigroups.

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