Theorems · Theorem · commutative algebra
Algebra.isAlgebraic_iff_isIntegral
∀ {K : Type u} {A : Type v} [inst : Field K] [inst_1 : Ring A] [inst_2 : Algebra K A],
Algebra.IsAlgebraic K A ↔ Algebra.IsIntegral K A- Defined in
- Mathlib.RingTheory.Algebraic.Integral
- Cited by
- 3 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- IsIntegralproof · cited by 427
- Algebra.IsAlgebraicstatement · cited by 322
- Algebra.IsIntegralstatement and proof · cited by 224
- IsAlgebraicproof · cited by 163
- isAlgebraic_iff_isIntegralproof · cited by 12
- Algebra.isIntegral_defproof · cited by 6
- Algebra.isAlgebraic_defproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- MvPolynomial.eq_vanishingIdeal_singleton_of_isMaximalproof · cited by 2
- exists_isTranscendenceBasis_and_isSeparable_of_perfectFieldproof · cited by 0