Theorems · Theorem · commutative algebra
IsAlgebraic.denominator_ne_zero
∀ (R : Type u_1) {S : Type u_2} [inst : CommRing R] [inst_1 : IsPrincipalIdealRing R] [inst_2 : CommRing S]
[inst_3 : Algebra R S] {x : S}, IsAlgebraic R x → Algebra.denominator R x ≠ 0- Defined in
- Mathlib.RingTheory.Algebraic.Denominator
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 140 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
- IsIntegralproof · cited by 427
- IsAlgebraicstatement and proof · cited by 163
- IsPrincipalIdealRingstatement and proof · cited by 131
- ne_zero_of_dvd_ne_zeroproof · cited by 26
- IsAlgebraic.exists_integral_multipleproof · cited by 8
- Algebra.denominatorstatement · cited by 5
- Algebra.denominator_dvd_iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- IsAlgebraic.natDenominator_ne_zeroproof · cited by 0