Normal bases for quadratic extensions inside cyclotomic fields
✍ Scribed by E. J. Gómez Ayala
- Publisher
- Springer
- Year
- 1996
- Tongue
- English
- Weight
- 142 KB
- Volume
- 66
- Category
- Article
- ISSN
- 0003-889X
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📜 SIMILAR VOLUMES
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Let `be a primitive 2 m th root of unity. We prove that Z[:]=Z [`] if and only if :=n\`i for some n, i # Z, i odd. This is the first example of number fields of arbitrarily large degree for which all power bases for the ring of integers are known. 2001 Academic Press ## 1. Introduction A number f
Cohen and McNay both give iterative constructions of irreducible polynomials of 2-power degree over finite fields of odd order. In this paper I show that the roots of these polynomials are completely normal elements in the appropriate extension field.