Displaying similar documents to “Approximatting rings of integers in number fields”

Topics in computational algebraic number theory

Karim Belabas (2004)

Journal de Théorie des Nombres de Bordeaux

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We describe practical algorithms from computational algebraic number theory, with applications to class field theory. These include basic arithmetic, approximation and uniformizers, discrete logarithms and computation of class fields. All algorithms have been implemented in the system.

An algorithm for primary decomposition in polynomial rings over the integers

Gerhard Pfister, Afshan Sadiq, Stefan Steidel (2011)

Open Mathematics

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We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals, resp. over finite fields, and the idea of Shimoyama-Yokoyama, resp. Eisenbud-Hunecke-Vasconcelos, to extract primary ideals from pseudo-primary ideals. A parallelized version of the algorithm is implemented in Singular. Examples and timings are given at the end of the article. ...

A remark on power series rings.

Paul M. Cohn (1992)

Publicacions Matemàtiques

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A trivializability principle for local rings is described which leads to a form of weak algorithm for local semifirs with a finitely generated maximal ideal whose powers meet in zero.