Titlebook: Advanced Topics in Computational Number Theory; Henri Cohen Textbook 2000 Springer Science+Business Media New York 2000 Euclidean algorith

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https://doi.org/10.1007/978-3-662-48347-3In Chapter 3 we studied variants of class and unit groups, the ray class groups .(.), as well as the associated unit groups .(.) of units multiplicatively congruent to 1 modulo m. The fundamental application of these notions through the deep theorems of class field theory is the construction of Abelian extensions.

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A. J. El Haj,K. Hampson,G. GogniatIn this appendix, we regroup and prove a number of results that we need.

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https://doi.org/10.1007/978-1-4615-0767-3n practice, however, number fields are frequently not given in this way. One of the most common other ways is to give a number field as a . extension, in other words as an algebra . over some base field . that is not necessarily equal to √. necessarily equal to ℚ. In this case, the basic algebraic o

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Bioreaction Engineering Principles, [Jan], or [Mart4] for more detailed statements and proofs. We present the results “à la Hasse”, without using ideles. This is more suitable for algorithmic treatment. For an idelic treatment, we refer to [Neu]. I have largely benefited from the notes of J. Martinet [Mart4] in writing this chapter.

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Zhi-Jun Zhang,Jiang Pan,Bao-Di Ma,Jian-He Xuor absolute discriminants. However, the algorithmic construction of these extensions is not completely straightforward. There are several ways to do this, but at present the most efficient general method is the use of Kummer extensions. In the next chapter, we will describe two other methods using a