Theorems · Definition · commutative algebra
Ideal.associatesNonZeroDivisorsEquivIsPrincipal
(R : Type u_1) →
[inst : CommRing R] → [IsDomain R] → Associates ↥(nonZeroDivisors R) ≃ { I // Submodule.IsPrincipal ↑I }A version of Ideal.associatesEquivIsPrincipal for non-zero-divisors generators.
- Defined in
- Mathlib.RingTheory.Ideal.IsPrincipal
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Equivstatement · cited by 8,337
- Submoduleproof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- Equiv.symmproof · cited by 3,681
- Submonoidstatement · cited by 3,086
- IsDomainstatement and proof · cited by 2,196
- nonZeroDivisorsstatement and proof · cited by 895
- Associatesstatement and proof · cited by 210
- Submodule.IsPrincipalstatement and proof · cited by 129
- MulEquiv.toEquivproof · cited by 126
- Equiv.subtypeEquivproof · cited by 32
Cited by7
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.fundamentalCone.integerSetEquivproof · cited by 2
- Ideal.associatesNonZeroDivisorsEquivIsPrincipal_coestatement · cited by 1
- Ideal.associatesNonZeroDivisorsEquivIsPrincipal_applystatement · cited by 0
- Ideal.associatesNonZeroDivisorsEquivIsPrincipal_map_onestatement · cited by 0
- Ideal.associatesNonZeroDivisorsEquivIsPrincipal_mulstatement · cited by 0
- Ideal.associatesNonZeroDivisorsMulEquivIsPrincipalproof · cited by 0
- Ideal.associatesNonZeroDivisorsEquivIsPrincipal.congr_simpstatement and proof · cited by 0