Kneser Field Extensions with Cogalois Correspondence

Albu, Toma; Nicolae, Florin

doi:10.1006/jnth.1995.1072

Cited by 16 publications

(9 citation statements)

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“…Theorem 0.1 [1,Theorem 3.7]. The following assertions are equivalent for a finite separable 2-radical extension F E with 2ÂF * finite and n=exp(2ÂF*):…”

Section: Preliminariesmentioning

confidence: 91%

“…and isomorphisms of lattices, inverse to one another? We were able to answer this question in [1] for separable 2-Kneser extensions:…”

Section: Preliminariesmentioning

confidence: 98%

“…Recall now some definitions from [1]. Let EÂF be a field extension; this extension is said to be a radical extension if there exists a subset A T(EÂF ) such that E=F(A), or equivalently, if E=F(T(EÂF )).…”

Section: Preliminariesmentioning

confidence: 99%

“…The aim of this paper is twofold: firstly, to extend all the main results of [4], established for simple radical extensions, to arbitrary finite radical extensions, and secondly to provide new characterizations of Kneser extensions and 2-Cogalois extensions introduced in [1], in terms of crossed homomorphisms.…”

Section: Introductionmentioning

confidence: 98%

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Finite Radical Field Extensions and Crossed Homomorphisms

Albu

Nicolae

1996

Journal of Number Theory

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“…Theorem 0.1 [1,Theorem 3.7]. The following assertions are equivalent for a finite separable 2-radical extension F E with 2ÂF * finite and n=exp(2ÂF*):…”

Section: Preliminariesmentioning

confidence: 91%

“…and isomorphisms of lattices, inverse to one another? We were able to answer this question in [1] for separable 2-Kneser extensions:…”

Section: Preliminariesmentioning

confidence: 98%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Finite Radical Field Extensions and Crossed Homomorphisms

Albu

Nicolae

1996

Journal of Number Theory

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“…There is no connection between the concepts of n-purity and quasi n-purity. The abstract notion of quasi n-purity goes back to the concept of n-purity from the field theoretic Cogalois Theory (see [1,3]). …”

Section: Definition 24 a Subgroup D Of An Abelian Group C Is Said Tmentioning

confidence: 99%

An Abstract Cogalois Theory for profinite groups

Albu¹,

Basarab²

2005

Journal of Pure and Applied Algebra

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The aim of this paper is to develop an abstract group theoretic framework for the Cogalois Theory of field extensions.The efforts to generalize the famous Gauss'Quadratic Reciprocity Law led to the Theory of Abelian extensions of global and local fields, known as Class Field Theory. This Theory can also be developed in an abstract group theoretic framework, namely for arbitrary profinite groups. Since the profinite groups are precisely those topological groups which arise as Galois groups of Galois extensions, an Abstract Galois Theory for arbitrary profinite groups was developed within the Abstract Class Field Theory (see e.g. [7]).The aim of this paper is to present a dual Theory, we called Abstract Cogalois Theory, to the Abstract Galois Theory. Roughly speaking, Cogalois Theory (see [2]) investigates field extensions, finite or not, which possess a Cogalois correspondence. This Theory is somewhat dual to the very classical Galois Theory dealing with field extensions possessing a Galois correspondence.

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