Theorems · Theorem · commutative algebra
IsDiscreteValuationRing.HasUnitMulPowIrreducibleFactorization.unique_irreducible
∀ {R : Type u_1} [inst : CommRing R],
IsDiscreteValuationRing.HasUnitMulPowIrreducibleFactorization R →
∀ ⦃p q : R⦄, Irreducible p → Irreducible q → Associated p q- Cited by
- 1 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- IsUnitproof · cited by 1,602
- add_commproof · cited by 1,535
- pow_zeroproof · cited by 1,094
- pow_oneproof · cited by 894
- Irreduciblestatement and proof · cited by 496
- Associatedstatement and proof · cited by 296
- pow_succ'proof · cited by 228
- lt_trichotomyproof · cited by 178
- Associated.symmproof · cited by 87
- Irreducible.ne_zeroproof · cited by 45
- Irreducible.not_isUnitproof · cited by 42
Cited by1
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.ofHasUnitMulPowIrreducibleFactorizationproof · cited by 0