Theorems · Theorem · field theory
AlgEquiv.isAlgebraic
∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] {B : Type u_2}
[inst_3 : Ring B] [inst_4 : Algebra R B] (e : A ≃ₐ[R] B) [Algebra.IsAlgebraic R A], Algebra.IsAlgebraic R BTransfer Algebra.IsAlgebraic across an AlgEquiv.
- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- AlgEquivstatement and proof · cited by 1,681
- AlgEquiv.symmproof · cited by 615
- Algebra.IsAlgebraicstatement and proof · cited by 322
- AlgEquiv.toAlgHomproof · cited by 273
- AlgEquiv.injectiveproof · cited by 61
- Algebra.IsAlgebraic.of_injectiveproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraicproof · cited by 5
- AlgEquiv.isAlgebraic_iffproof · cited by 1
- Algebra.isGeometricallyReduced_field_iffproof · cited by 1
- RatFunc.isAlgebraic_adjoin_simple_X'proof · cited by 0
- Algebra.IsPushout.isAlgebraicproof · cited by 0
- Algebra.IsPushout.isAlgebraic'proof · cited by 0