Theorems · Theorem · commutative algebra

emultiplicity_eq_emultiplicity_span

Deprecated since 2026-04-16Use Ideal.emultiplicity_eq_emultiplicity_span instead.

∀ {R : Type u_1} [inst : CommRing R] [IsDomain R] [IsPrincipalIdealRing R] {a b : R},
  emultiplicity (Ideal.span {a}) (Ideal.span {b}) = emultiplicity a b

Alias of Ideal.emultiplicity_eq_emultiplicity_span.

Defined in: Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas
Cited by: 0 results in Mathlib
Foundations: Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDomain IsPrincipalIdealRing

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Setstatement · cited by 53,352
CommRingstatement · cited by 17,173
ENatstatement · cited by 4,985
Idealstatement · cited by 4,748
IsDomainstatement · cited by 2,196
Ideal.spanstatement · cited by 948
emultiplicitystatement · cited by 156
IsPrincipalIdealRingstatement · cited by 131
Ideal.emultiplicity_eq_emultiplicity_spanproof · cited by 3

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