Theorems · Theorem · commutative algebra
IsBezout.span_gcd_eq_span_gcd
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsBezout R] [IsDomain R] [inst_3 : GCDMonoid R] (x y : R),
Ideal.span {gcd x y} = Ideal.span {IsBezout.gcd x y}- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Idealstatement · cited by 4,748
- IsDomainstatement and proof · cited by 2,196
- Ideal.spanstatement · cited by 948
- GCDMonoid.gcdstatement · cited by 143
- GCDMonoidstatement and proof · cited by 96
- GCDMonoid.gcd_dvd_leftproof · cited by 36
- GCDMonoid.gcd_dvd_rightproof · cited by 34
- associated_of_dvd_dvdproof · cited by 28
- IsBezoutstatement and proof · cited by 23
- GCDMonoid.dvd_gcdproof · cited by 23
Cited by1
Results whose statement or proof uses this declaration.
- span_gcdproof · cited by 2