منابع مشابه
Remarks on normal bases
We prove that any Galois extension of commutative rings with normal basis and abelian Galois group of odd order has a self dual normal basis. Also we show that if S/R is an unramified extension of number rings with Galois group of odd order and R is totally real then the normal basis does not exist for S/R.
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Let K⊂L be a finite Galois extension of fields, of degree n. Let G be the Galois group, and let (σα)σ∈G be a normal basis for L over K. An argument due to Mullin, Onyszchuk, Vanstone and Wilson (Discrete Appl. Math. 22 (1988/89), 149–161) shows that the matrix that describes the map x7→αx on this basis has at least 2n−1 non-zero entries. If it contains exactly 2n−1 non-zero entries, then the no...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 2001
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm87-1-4