Theorems · Theorem · field theory
Subalgebra.isAlgebraic_iff
∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] (S : Subalgebra R A),
S.IsAlgebraic ↔ Algebra.IsAlgebraic R ↥SA subalgebra is algebraic if and only if it is algebraic as an algebra.
- Defined in
- Mathlib.RingTheory.Algebraic.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Polynomialproof · cited by 5,681
- map_zeroproof · cited by 1,614
- Subalgebrastatement and proof · cited by 1,353
- Polynomial.aevalproof · cited by 615
- Algebra.IsAlgebraicstatement and proof · cited by 322
- Subtype.val_injectiveproof · cited by 232
- IsAlgebraicproof · cited by 163
- Subalgebra.valproof · cited by 104
Cited by1
Results whose statement or proof uses this declaration.
- IsAlgebraic.adjoin_of_forall_isAlgebraicproof · cited by 1