Theorems · Theorem · commutative algebra
Submodule.IsPrincipal.associated_generator_span_self
∀ {R : Type u} [inst : CommSemiring R] [IsDomain R] (r : R),
Associated (Submodule.IsPrincipal.generator (Ideal.span {r})) r- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringIsDomain
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- IsDomainstatement and proof · cited by 2,196
- Ideal.spanstatement and proof · cited by 948
- Associatedstatement · cited by 296
- Submodule.IsPrincipal.generatorstatement · cited by 56
- Ideal.span_singleton_generatorproof · cited by 17
- Ideal.span_singleton_eq_span_singletonproof · cited by 15
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