Theorems · Theorem · commutative algebra
IsDiscreteValuationRing.irreducible_of_span_eq_maximalIdeal
∀ {R : Type u_1} [inst : CommSemiring R] [inst_1 : IsLocalRing R] [IsDomain R] (ϖ : R),
ϖ ≠ 0 → IsLocalRing.maximalIdeal R = Ideal.span {ϖ} → Irreducible ϖ- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- IsDomainstatement and proof · cited by 2,196
- IsUnitproof · cited by 1,602
- Ideal.spanstatement and proof · cited by 948
- Irreduciblestatement · cited by 496
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- Submodule.mem_span_singleton_selfproof · cited by 59
- isUnit_of_dvd_oneproof · cited by 18
- Ideal.mem_span_singleton'proof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.irreducible_iff_uniformizerproof · cited by 4
- exists_maximalIdeal_pow_eq_of_principalproof · cited by 1