Theorems · Theorem · field theory
IsAlgebraic.algebraMap
∀ {R : Type u} {S : Type u_1} {A : Type v} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Ring A]
[inst_3 : Algebra R A] [inst_4 : Algebra R S] [inst_5 : Algebra S A] [IsScalarTower R S A] {a : S},
IsAlgebraic R a → IsAlgebraic R ((algebraMap S A) a)- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialproof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- map_zeroproof · cited by 1,614
- Polynomial.aevalproof · cited by 615
- IsAlgebraicstatement and proof · cited by 163
- Polynomial.aeval_algebraMap_applyproof · cited by 24
Cited by2
Results whose statement or proof uses this declaration.
- Valuation.transcendental_of_ne_oneproof · cited by 0
- IsFractionRing.isAlgebraic_iff'proof · cited by 0