Theorems · Theorem · commutative algebra
Ideal.associatesEquivIsPrincipal_mul
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] (x y : Associates R),
↑((Ideal.associatesEquivIsPrincipal R) (x * y)) =
↑((Ideal.associatesEquivIsPrincipal R) x) * ↑((Ideal.associatesEquivIsPrincipal R) y)- Defined in
- Mathlib.RingTheory.Ideal.IsPrincipal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Equivstatement · cited by 8,337
- Idealstatement · cited by 4,748
- IsDomainstatement and proof · cited by 2,196
- Ideal.spanproof · cited by 948
- Associatesstatement and proof · cited by 210
- Associates.mkproof · cited by 137
- Submodule.IsPrincipalstatement · cited by 129
- Quot.outproof · cited by 14
- Ideal.span_singleton_mul_span_singletonproof · cited by 12
- Ideal.associatesEquivIsPrincipalstatement and proof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.associatesNonZeroDivisorsEquivIsPrincipal_mulproof · cited by 0