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Diff — Field extension

Revision #3104 → #3610 · back to history

addedTower of extensions56230deca0d1
modifiedOnly finite extension of R is C (Frobenius)a6b21879a7ed
FieldFrom #3104To #3610
mathlib.declReal.nonempty_algEquiv_or
mathlib.match_kindgeneralization
mathlib.moduleMathlib.Analysis.Complex.Polynomial.Basic
noteFrobenius's theorem that the only finite field extensions of ℝ are ℝ and ℂ is not (as of review) packaged in Mathlib.`Real.nonempty_algEquiv_or` states every algebraic (hence finite) extension of ℝ is algebra-isomorphic to ℝ or ℂ, covering the Frobenius statement.
statusnot_formalizedformalized
modifiedAzumaya algebra274ae3c887ea
FieldFrom #3104To #3610
mathlib.declIsAzumaya
mathlib.match_kindexact
mathlib.moduleMathlib.Algebra.Azumaya.Defs
noteAzumaya algebras (CSA-analogue over commutative local rings) do not appear to have a dedicated definition in Mathlib at the time of review.`IsAzumaya R A` in `Mathlib.Algebra.Azumaya.Defs` formalizes Azumaya algebras via bijectivity of the left-right multiplication map on a projective, faithful, finitely generated module.
statusnot_formalizedformalized