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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.