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Calculs d'invariants primitifs de groupes finis

Ines Abdeljaouad (2010)

RAIRO - Theoretical Informatics and Applications

We introduce in this article a new method to calculate all absolute and relatif primitive invariants of finite groups. This method is inspired from K. Girstmair which calculate an absolute primitive invariant of minimal degree. Are presented two algorithms, the first one enable us to calculate all primitive invariants of minimal degree, and the second one calculate all absolute or relative primitive invariants with distincts coefficients. This work take place in Galois Theory and Invariant Theory. ...

Cale Bases in Algebraic Orders

Martine Picavet-L’Hermitte (2003)

Annales mathématiques Blaise Pascal

Let R be a non-maximal order in a finite algebraic number field with integral closure R ¯ . Although R is not a unique factorization domain, we obtain a positive integer N and a family 𝒬 (called a Cale basis) of primary irreducible elements of R such that x N has a unique factorization into elements of 𝒬 for each x ∈ R coprime with the conductor of R . Moreover, this property holds for each nonzero x ∈ R when the natural map Spec ( R ¯ ) → Spec ( R ) is bijective. This last condition is actually equivalent to several properties linked...

Characteristic of Rings. Prime Fields

Christoph Schwarzweller, Artur Korniłowicz (2015)

Formalized Mathematics

The notion of the characteristic of rings and its basic properties are formalized [14], [39], [20]. Classification of prime fields in terms of isomorphisms with appropriate fields (ℚ or ℤ/p) are presented. To facilitate reasonings within the field of rational numbers, values of numerators and denominators of basic operations over rationals are computed.

Classe de conjugaison du frobenius des variétés abéliennes à réduction ordinaire

Rutger Noot (1995)

Annales de l'institut Fourier

Soient X une variété abélienne sur un corps de nombres E et G son groupe de Mumford–Tate. Soit v une valuation de E et pour tout nombre premier ℓ tel que v ( ℓ ) = 0 , soit F ℓ ∈ G ( Q ℓ ) l’automorphisme de Frobenius (géométrique) de la cohomologie étale ℓ -adique de X . On montre que si X a une bonne réduction ordinaire en v , alors il existe F ∈ G ( Q ) tel que, pour tout ℓ , F ℓ soit conjugué à F dans G ( Q ℓ ) . On montre un résultat analogue pour le frobenius de la cohomologie cristalline de la réduction de X modulo v .

Classes of Commutative Clean Rings

Wolf Iberkleid, Warren Wm. McGovern (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Let A be a commutative ring with identity and I an ideal of A . A is said to be I - c l e a n if for every element a ∈ A there is an idempotent e = e 2 ∈ A such that a - e is a unit and a e belongs to I . A filter of ideals, say ℱ , of A is Noetherian if for each I ∈ ℱ there is a finitely generated ideal J ∈ ℱ such that J ⊆ I . We characterize I -clean rings for the ideals 0 , n ( A ) , J ( A ) , and A , in terms of the frame of multiplicative Noetherian filters of ideals of A , as well as in terms of more classical ring properties.

Clôture intégrale des idéaux et équisingularité

Monique Lejeune-Jalabert, Bernard Teissier (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

This text has two parts. The first one is the essentially unmodified text of our 1973-74 seminar on integral dependence in complex analytic geometry at the Ecole Polytechnique with J-J. Risler’s appendix on the Łojasiewicz exponents in the real-analytic framework. The second part is a short survey of more recent results directly related to the content of the seminar.The first part begins with the definition and elementary properties of the ν ¯ order function associated to an ideal I of a reduced analytic...

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