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Theorems · Theorem · commutative algebra

UniqueFactorizationMonoid.ne_zero_of_mem_factors

∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] {p a : α},
  p ∈ UniqueFactorizationMonoid.factors a → a ≠ 0
Defined in
Mathlib.RingTheory.UniqueFactorizationDomain.Defs
Cited by
3 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidWithZeroUniqueFactorizationMonoid
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Around this declaration

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

UniqueFactorizationMonoid.prime_of_factor · cited by 9UniqueFactorizationMonoid…UniqueFactorizationMonoid.dvd_of_mem_factors · cited by 5UniqueFactorizationMonoid…Ideal.Factors.ramificationIdx_ne_zero · cited by 0Factors.ramificationIdx_n…Multiset · cited by 2627MultisetCommMonoidWithZero · cited by 913CommMonoidWithZeroUniqueFactorizationMonoid · cited by 279UniqueFactorizationMonoidUniqueFactorizationMonoid.factors · cited by 55UniqueFactorizationMonoid…UniqueFactorizationMonoid.factors_zero · cited by 4UniqueFactorizationMonoid…UniqueFactorizationMonoid.ne_…CITED BYCITES

Cites5

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Cited by3

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