On a Theorem of Childs on Normal Bases of Rings of Integers: Addendum | Zendy

Ichimura Humio | Zendy

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On a Theorem of Childs on Normal Bases of Rings of Integers: Addendum

Author(s) -

Ichimura Humio

Publication year - 2004

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/s0024610703005076

Subject(s) - addendum , mathematics , extension (predicate logic) , assertion , prime (order theory) , basis (linear algebra) , algebraic number field , field (mathematics) , pure mathematics , combinatorics , discrete mathematics , philosophy , computer science , geometry , linguistics , programming language

Let p ⩾ 3 be a prime number, F be a number field with ζ p ∉ F × , and K = F (ζ p ). In a previous paper, the author proved, under some assumption on p and F , that an unramified cyclic extension N / F of degree p has a normal integral basis if and only if the pushed‐up extension NK / K has a normal integral basis. This addendum shows that the assertion holds without the above‐mentioned assumption.

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