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Algebraic number-fields

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Basic Number Theory

Part of the book series: Classics in Mathematics ((GL))


We shall need some elementary results about vector-spaces over Q, involving the following concept:

  1. Definition 1.

    Let E be a vector-space of finite dimension over Q. By a Q-lattice in E, we understand a finitely generated subgroup of E which contains a basis of E over Q.

  2. Proposition 1.

    Let E be a vector-space of finite dimension over Q; let L, L’ be two Q-lattices in E. Then there is an integer m>0 such that mLL’.

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© 1995 Springer-Verlag Berlin Heidelberg

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Weil, A. (1995). Algebraic number-fields. In: Basic Number Theory. Classics in Mathematics. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58655-5

  • Online ISBN: 978-3-642-61945-8

  • eBook Packages: Springer Book Archive

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