Theorems · Theorem · commutative algebra
IsAlgebraic.iff_exists_smul_integral
∀ {R : Type u_1} {A : Type u_3} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] {z : A} [IsReduced R],
IsAlgebraic R z ↔ ∃ y, y ≠ 0 ∧ IsIntegral R (y • z)- Defined in
- Mathlib.RingTheory.Algebraic.Integral
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- IsIntegralstatement and proof · cited by 427
- IsAlgebraicstatement and proof · cited by 163
- IsReducedstatement and proof · cited by 98
- isNilpotent_iff_eq_zeroproof · cited by 9
- IsAlgebraic.exists_integral_multipleproof · cited by 8
- IsAlgebraic.of_smul_isIntegralproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IsAlgebraic.mulproof · cited by 5
- IsAlgebraic.addproof · cited by 3