1. n. (algebra, Galois theory) (of a polynomial) Given a polynomial p over a field K, the smallest extension field L of K such that p, as a polynomial over L, decomposes into linear factors (polynomials of
2. n. (algebra, ring theory, of a K-algebra) Given a finite-dimensional K-algebra (algebra over a field), an extension field whose every simple (indecomposable) module is absolutely simple (remains simple a
The terminology "splitting field of a K-algebra" is motivated by the same terminology regarding a polynomial. A splitting field of a K-algebraA is a field extensionK\mapsto L such thatA\otimes_
3. n. (algebra, ring theory, of a central simple algebra) Given a central simple algebra A over a field K, another field, E, such that the tensor product A⊗E is isomorphic to a matrix ring over E.
Every finite dimensional central simple algebra has a splitting field: moreover, if said CSA is a division algebra, then a maximal subfield of it is a splitting field.
4. n. (algebra, character theory) (of a character χ of a representation of a group G) A field K over which a K-representation of G exists which includes the character χ; (of a group G) a field over which a
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splitting
1. n. (Industrie) Dissociation.
2. v. Participe présent du verbe to split.
split
1. v. Fendre.
He busied himself splitting wood for the fire.
Il s'occupa à couper du bois pour le feu.
2. v. Diviser, se diviser.
The developers split the property into tiny lots, and cut down all the trees.
Souvent, dans l'été, je quitte mon logis dès l'aube du matin, et j'erre tout le long du jour par les champs et les ruelles écartées, ou même je m'échappe durant plusieurs journées ou plusieurs semaines de suite ; …
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