From Field Theoretic to Abstract Co-Galois Theory
DOI10.1016/S1570-7954(07)05001-2zbMath1197.12002MaRDI QIDQ3053869
Publication date: 30 October 2010
Published in: Handbook of Algebra (Search for Journal in Brave)
Galois cohomologyGalois groupGalois connectionKummer theoryGalois extensionGalois theoryHopf algebracohomology groupfield extensionalgebraic number fieldfieldprofinite groupPontryagin dualityAbelian extensionradical extensiongroup-graded algebracrossed homomorphismco-Galois extensionco-Galois groupKneser criterion\(G\)-co-Galois extensionabstract co-Galois theoryco-Galois connectionco-Galois group of cocyclesco-Galois theoryKneser extensionkneser group of cocyclesKummer group of cocyclespurity criterionstrongly Kneser extension
Separable extensions, Galois theory (12F10) Limits, profinite groups (20E18) Hopf algebras and their applications (16T05) Research exposition (monographs, survey articles) pertaining to field theory (12-02)
Cites Work
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- Biinvertible actions of Hopf algebras
- The torsion group of a field defined by radicals
- Field theoretic cogalois theory via abstract cogalois theory
- Cogalois theory for field extensions
- Several results on radical extensions
- A Galois correspondence for radical extensions of fields
- Finite radical field extensions and crossed homomorphisms
- Group-graded rings and modules
- The torsion group of a radical extension
- Körper, über denen alle algebraischen Erweiterungen der Kummer'schen Theorie genügen
- The lattice of subfields of a radical extension
- On cogalois extensions
- Kummer extensions with few roots of unity
- An application of Galois theory to elementary arithmetic
- On the degree of the splitting field of an irreducible binomial
- On Kneser extensions
- Some results on radical extensions
- Radicals of binomial ideals
- Brauer groups, Hopf algebras and Galois theory
- Hopf Galois theory for separable field extensions
- Kneser field extensions with cogalois correspondence
- Allowable groups and cogalois extensions
- Subgroup lattices of groups
- An abstract cogalois theory for profinite groups.
- Théoremes de finitude en cohomologie galoisienne
- Isomorphisms of Clifford extensions
- On a fundamental inequality in number theory
- Compounding Clifford's theory
- On the degree of extensions generated by finitely many algebraic numbers
- On the linear independence of algebraic numbers
- Ein Darstellungssatz für kompakte, total unzusammenhängende Gruppen
- Correction to the paper "Structure theorems for radical extensions of fields", Acta Arith. 38 (1980), pp. 111-115
- Über Radikalerweiterungen
- On normal binomials
- Structure theorems for radical extensions of fields
- Lineare Abhängigkeit von Wurzeln
- The Degrees of Radical Extensions
- On linear dependence of roots
- Multiplicative Groups Under Field Extension
- Abelian binomials, power residues and exponential congruences
- On subfÌields of radical extensions
- ON RADICAL FIELD EXTENSIONS OF PRIME EXPONENT
- LATTICE-ISOMORPHIC GROUPS, AND INFINITE ABELIAN G-COGALOIS FIELD EXTENSIONS
- SOME EXAMPLES IN COGALOIS THEORY WITH APPLICATIONS TO ELEMENTARY FIELD ARITHMETIC
- INFINITE COGALOIS THEORY, CLIFFORD EXTENSIONS, AND HOPF ALGEBRAS
- Covering morphisms
- INFINITE FIELD EXTENSIONS WITH COGALOIS CORRESPONDENCE
- Cogalois extensions via strongly graded fields
- Heckesche Systeme idealer Zahlen und Knesersche Körpererweiterungen
- Compact coGalois groups
- Algebraische Abhängigkeit von Wurzeln
- On the Linear Independence of Fractional Powers of Integers
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