Theorems · Theorem · commutative algebra
IsAlgebraic.exists_integral_multiple
∀ {R : Type u_1} {A : Type u_3} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] {z : A},
IsAlgebraic R z → ∃ y, y ≠ 0 ∧ IsIntegral R (y • z)- Defined in
- Mathlib.RingTheory.Algebraic.Integral
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Moduleproof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommMonoidproof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringproof · cited by 10,911
- Ringstatement and proof · cited by 7,463
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerproof · cited by 3,896
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.aevalproof · cited by 615
Cited by8
Results whose statement or proof uses this declaration.
- IsAlgebraic.mulproof · cited by 5
- IsAlgebraic.restrictScalars_of_isIntegralproof · cited by 4
- IsAlgebraic.addproof · cited by 3
- IsAlgebraic.iff_exists_smul_integralproof · cited by 2
- IsIntegralClosure.isFractionRing_of_algebraicproof · cited by 2
- Algebra.IsAlgebraic.exists_integral_multiplesproof · cited by 2
- IsAlgebraic.denominator_ne_zeroproof · cited by 1
- IsAlgebraic.exists_smul_eqproof · cited by 1