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Qu'est-ce (qui) est extension$26894$ - définition
FIELD EXTENSION WHOSE GALOIS GROUP IS ABELIAN
Cyclic extension; Abelian extensions; Abelian Extension; Cyclotomic extension; Solvable extension; Cyclic field extension; Abelian field extension; Solvable field extension
Group extension
GROUP FOR WHICH A GIVEN GROUP IS A NORMAL SUBGROUP
Extension problem; Extension (algebra); Split extension; Extension of a group; Central extension (mathematics)
In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence
Extension (metaphysics)
THE PROPERTY OF STRETCHING OUT OR TAKING UP SPACE
Physical extension
In metaphysics, extension signifies both 'stretching out' (Latin: extensio) as well as later 'taking up space', and most recently, spreading one's internal mental cognition into the external world.
Field extension
PAIR OF A MATHEMATICAL FIELD AND ITS SUBFIELD
Subfield (mathematics); Quadratic extension; Purely transcendental; Extension field; Quadratic field extension; Degree (field theory); Subextension (field theory); Trivial extension; Intermediate field; Adjunction (field theory); Extension of a field; Finitely generated field extension; Purely transcendental extension; Field Extension; Finitely generated extension; Subextension; Cubic field extension; Cubic extension; Transcendental field extension; Adjoining (field theory)
In mathematics, particularly in algebra, a field extension is a pair of fields E\subseteq F, such that the operations of E are those of F restricted to E. In this case, F is an extension field of E and E is a subfield of F.
Wikipédia
Abelian extension
In abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is also cyclic, the extension is also called a cyclic extension. Going in the other direction, a Galois extension is called solvable if its Galois group is solvable, i.e., if the group can be decomposed into a series of normal extensions of an abelian group. Every finite extension of a finite field is a cyclic extension.
