Key Words: Field extension, radical extension, Kneser extension, strongly Kneser extension, Kneser Criterion, Galois extension, Cogalois extension, -Cogalois extension, Galois Theory, Cogalois Theory, Galois group, Cogalois group, Kneser group, Kummer Theory, Abelian extension, profinite group, crossed homomorphism, algebraic number field, group-graded algebra, Hopf algebra, Abstract Cogalois Theory.
2000 Mathematics Subject Classification: Primary: 12-02;
Secondary: 12E30, 12F05, 12F10, 12F99, 16W50, 20E18, 20J06.
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