Abstract
Let F be a finite field (commutative or not) with the unit-element 1. Its characteristic must clearly be a prime p > l, and the prime ring in F is isomorphic to the prime field F p =Z/p Z, with which we may identify it. Then F may be regarded as a vector-space over F p ; as such, it has an obviously finite dimension ƒ, and the number of its elements is q=p f. If F is a subfield of a field F′; with q′=p f ′ elements, F&#x 2032; may also be regarded e.g. as a left vector-space over F; if its dimension as such is d, we have f′ = df and q′ = q d =p df.
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© 1973 Springer Science+Business Media New York
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Weil, A. (1973). Locally compact fields. In: Basic Number Theory. Die Grundlehren der mathematischen Wissenschaften, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05978-4_1
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DOI: https://doi.org/10.1007/978-3-662-05978-4_1
Publisher Name: Springer, Berlin, Heidelberg
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