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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 → Prop

A 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
Assumes
CommRingRingAlgebra

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.