Abstract
Let F be a finite field (commutative or not) with the unit-element 1. Its characteristic must clearly be a prime p > 1, and the prime ring in F is isomorphic to the prime field Fp = Z/pZ, with which we may identify it. Then F may be regarded as a vector-space over Fp; as such, it has an obviously finite dimension f, and the number of its elements is q = pf. If F is a subfield of a field F’ with q’ = pf’ elements, F’ 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’ = qd = pdf.
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© 1995 Springer-Verlag Berlin Heidelberg
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Weil, A. (1995). Locally compact fields. In: Basic Number Theory. Classics in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61945-8_1
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DOI: https://doi.org/10.1007/978-3-642-61945-8_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58655-5
Online ISBN: 978-3-642-61945-8
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