A matrix criterion for normal integral bases
نویسندگان
چکیده
منابع مشابه
Counting Generators of Normal Integral Bases
We present a very accurate formula counting norms of normal integral bases in tame abelian extensions of the rational eld. The methods used include applications of Schmidt's Subspace Theorem, Baker's Theorem and the Hardy-Littlewood Method, all from diophantine approximation.
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A new criterion on normal bases of finite field extension Fqn/Fq is presented and explicit criterions for several particular finite field extensions are derived from this new criterion.
متن کاملNormal integral bases for A4 extensions of the rationals
We give an algorithm for constructing normal integral bases of tame Galois extensions of the rationals with group A4. Using earlier works we can do the same until degree 15.
متن کاملNon-existence and Splitting Theorems for Normal Integral Bases
We establish new conditions that prevent the existence of (weak) normal integral bases in tame Galois extensions of number fields. This leads to the following result: under appropriate technical hypotheses, the existence of a normal integral basis in the upper layer of an abelian tower Q ⊂ K ⊂ L forces the tower to be split in a very strong sense.
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1978
ISSN: 0019-2082
DOI: 10.1215/ijm/1256048474