Theorems · Theorem · commutative algebra
IsBezout.gcd_dvd_right
∀ {R : Type u} [inst : CommRing R] (x y : R) [inst_1 : Submodule.IsPrincipal (Ideal.span {x, y})], IsBezout.gcd x y ∣ y- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Submodule.IsPrincipalstatement and proof · cited by 129
- Ideal.subset_spanproof · cited by 86
- IsBezout.gcdstatement · cited by 12
- Submodule.IsPrincipal.mem_iff_generator_dvdproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- IsRelPrime.isCoprimeproof · cited by 5
- IsBezout.associated_gcd_gcdproof · cited by 1
- IsBezout.span_gcd_eq_span_gcdproof · cited by 1