Abstract
Let k be a commutative field. An absolute value on k is a function k → R+ denoted by x ↦ |x|, x ∈ k satisfying the conditions:
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1.
|x| = 0 ⇔ x = 0.
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2.
|xy| = |x||y|.
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3.
|1| = 1.
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4.
|x + y| ≤ |x| + |y|.
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© 1992 Springer-Verlag Berlin Heidelberg
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Serre, JP. (1992). Complete Fields. In: Lie Algebras and Lie Groups. Lecture Notes in Mathematics, vol 1500. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70634-2_8
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DOI: https://doi.org/10.1007/978-3-540-70634-2_8
Publisher Name: Springer, Berlin, Heidelberg
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