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Displaying similar documents to “Normal integral bases for infinite abelian extensions”

Inverse property of nonassociative abelian extensions

Ágota Figula, Péter T. Nagy (2020)

Commentationes Mathematicae Universitatis Carolinae

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Our paper deals with the investigation of extensions of commutative groups by loops so that the quasigroups that result in the multiplication between cosets of the kernel subgroup are T-quasigroups. We limit our study to extensions in which the quasigroups determining the multiplication are linear functions without constant term, called linear abelian extensions. We characterize constructively such extensions with left-, right-, or inverse properties using a general construction according...

Linear extensions of orders invariant under abelian group actions

Alexander R. Pruss (2014)

Colloquium Mathematicae

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Let G be an abelian group acting on a set X, and suppose that no element of G has any finite orbit of size greater than one. We show that every partial order on X invariant under G extends to a linear order on X also invariant under G. We then discuss extensions to linear preorders when the orbit condition is not met, and show that for any abelian group acting on a set X, there is a linear preorder ≤ on the powerset 𝓟X invariant under G and such that if A is a proper subset of B, then...

Remarks on normal bases

Marcin Mazur (2001)

Colloquium Mathematicae

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We prove that any Galois extension of a commutative ring with a normal basis and abelian Galois group of odd order has a self-dual normal basis. We apply this result to get a very simple proof of nonexistence of normal bases for certain extensions which are of interest in number theory.