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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 tel que v ( ) = 0 , soit F G ( Q ) l’automorphisme de Frobenius (géométrique) de la cohomologie étale -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 , F soit conjugué à F dans G ( Q ) . 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 , of A is Noetherian if for each I there is a finitely generated ideal J 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...

Cohen-Macaulayness of multiplication rings and modules

R. Naghipour, H. Zakeri, N. Zamani (2003)

Colloquium Mathematicae

Let R be a commutative multiplication ring and let N be a non-zero finitely generated multiplication R-module. We characterize certain prime submodules of N. Also, we show that N is Cohen-Macaulay whenever R is Noetherian.

Commutative graded- S -coherent rings

Anass Assarrar, Najib Mahdou, Ünsal Tekir, Suat Koç (2023)

Czechoslovak Mathematical Journal

Recently, motivated by Anderson, Dumitrescu’s S -finiteness, D. Bennis, M. El Hajoui (2018) introduced the notion of S -coherent rings, which is the S -version of coherent rings. Let R = α G R α be a commutative ring with unity graded by an arbitrary commutative monoid G , and S a multiplicatively closed subset of nonzero homogeneous elements of R . We define R to be graded- S -coherent ring if every finitely generated homogeneous ideal of R is S -finitely presented. The purpose of this paper is to give the graded...

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