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Theorems · Definition · commutative algebra

Associates.FactorSet.prod

{α : Type u_1} → [inst : CommMonoidWithZero α] → Associates.FactorSet α → Associates α

Evaluates the product of a FactorSet to be the product of the corresponding multiset, or 0 if there is none.

Defined in
Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet
Cited by
20 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext, Quot.sound
Assumes
CommMonoidWithZero
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Associates.factors_prod · cited by 9Associates.factors_prodAssociates.factors_one · cited by 6Associates.factors_oneAssociates.FactorSet.unique · cited by 5FactorSet.uniqueAssociates.factors_mul · cited by 4Associates.factors_mulAssociates.eq_of_factors_eq_factors · cited by 4Associates.eq_of_factors_…Associates.prod_coe · cited by 3Associates.prod_coeAssociates.prod_factors · cited by 3Associates.prod_factorsAssociates.factors_le · cited by 2Associates.factors_leAssociates.factors_prime_pow · cited by 2Associates.factors_prime_…Associates.prod_mono · cited by 2Associates.prod_monoAssociates.FactorSet.prod.eq_def · cited by 2prod.eq_defAssociates.prod_add · cited by 2Associates.prod_addAssociates.dvd_of_mem_factors · cited by 2Associates.dvd_of_mem_fac…Associates.FactorSet.prod_eq_zero_iff · cited by 2FactorSet.prod_eq_zero_iffAssociates.prod_top · cited by 2Associates.prod_topMultiset · cited by 2627MultisetCommMonoidWithZero · cited by 913CommMonoidWithZeroMultiset.map · cited by 876Multiset.mapMultiset.prod · cited by 528Multiset.prodIrreducible · cited by 496IrreducibleAssociates · cited by 210AssociatesAssociates.FactorSet · cited by 52Associates.FactorSetFactorSet.prodCITED BYCITES

Cites7

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Cited by20

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