Theorems · Theorem · commutative algebra
Ideal.emultiplicity_eq_emultiplicity_span
∀ {R : Type u_1} [inst : CommRing R] [IsDomain R] [IsPrincipalIdealRing R] {a b : R},
emultiplicity (Ideal.span {a}) (Ideal.span {b}) = emultiplicity a b- Cited by
- 3 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Top.topproof · cited by 9,680
- ENatstatement and proof · cited by 4,985
- Idealstatement and proof · cited by 4,748
- IsDomainstatement and proof · cited by 2,196
- Ideal.spanstatement and proof · cited by 948
- emultiplicitystatement and proof · cited by 156
- IsPrincipalIdealRingstatement and proof · cited by 131
- multiplicityproof · cited by 117
- lt_add_oneproof · cited by 105
- FiniteMultiplicityproof · cited by 73
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.count_span_normalizedFactors_eqproof · cited by 2
- emultiplicity_eq_emultiplicity_spanproof · cited by 0