Theorems · Theorem · commutative algebra
IsBezout.associated_gcd_gcd
∀ (R : Type u) [inst : CommRing R] {x y : R} [inst_1 : Submodule.IsPrincipal (Ideal.span {x, y})]
[inst_2 : GCDMonoid R], Associated (IsBezout.gcd x y) (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.
Cites12
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
- Ideal.spanstatement and proof · cited by 948
- Associatedstatement · cited by 296
- GCDMonoid.gcdstatement · cited by 143
- Submodule.IsPrincipalstatement and proof · cited by 129
- GCDMonoidstatement and proof · cited by 96
- IsBezout.gcdstatement · cited by 12
- IsBezout.gcd_dvd_leftproof · cited by 3
- IsBezout.gcd_dvd_rightproof · cited by 3
- IsBezout.dvd_gcdproof · cited by 2
- gcd_greatest_associatedproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Finset.gcd_eq_sum_mulproof · cited by 1