Theorems · Definition · field theory
Subalgebra.IsAlgebraic
{R : Type u} → {A : Type v} → [inst : CommRing R] → [inst_1 : Ring A] → [inst_2 : Algebra R A] → Subalgebra R A → PropA subalgebra is algebraic if all its elements are algebraic.
- Defined in
- Mathlib.RingTheory.Algebraic.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Subalgebrastatement and proof · cited by 1,353
- IsAlgebraicproof · cited by 163
Cited by7
Results whose statement or proof uses this declaration.
- isAlgebraic_solvableByRadstatement · cited by 2
- Algebra.isAlgebraic_adjoin_iffstatement · cited by 2
- Subalgebra.IsAlgebraic.toIntermediateFieldstatement and proof · cited by 1
- Algebra.isAlgebraic_adjoin_of_nonemptystatement and proof · cited by 1
- Algebra.isAlgebraic_adjoin_singleton_iffstatement · cited by 1
- Subalgebra.isAlgebraic_iffstatement · cited by 1
- Algebra.isAlgebraic_iffstatement · cited by 0