Structures · Algebra
IsDecompositionField
Let L/K be a Galois extension of fields and let P be a prime ideal of B. The predicate that
says that D is the decomposition field of P in L/K, that is the subfield fixed by the
decomposition subgroup of P, that is the stabilizer of P in Gal(L/K).
- Shape
- 4 explicit arguments
Extends1
Extended by0
Nothing extends this class yet.
Concrete types that are instances0
No instance on a concrete type; it is reached through other classes.
How is a type an instance?
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Assumed by12
- IsDecompositionField.ringEquiv
- IsDecompositionField.ramificationIdxIn_eq
- IsDecompositionField.rank_left
- IsDecompositionField.rank_right
- IsDecompositionField.inertiaDegIn_eq
- IsDecompositionField.algebraMap_ringEquiv_apply
- IsDecompositionField.ramificationIdx_eq
- IsInertiaField.rank_decompositionField
- IsDecompositionField.inertiaDeg_eq
- IsDecompositionField.algebraMap_ringEquiv_symm_apply
- IsDecompositionField.primesOver_eq_singleton
- IsDecompositionField.toIsGaloisGroup