Theorems · Theorem · commutative algebra
Ideal.isMaximal_def
∀ {α : Type u} [inst : Semiring α] {I : Ideal α}, I.IsMaximal ↔ IsCoatom I- Defined in
- Mathlib.RingTheory.Ideal.Maximal
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- Ideal.IsMaximalstatement and proof · cited by 452
- IsCoatomstatement and proof · cited by 114
- Ideal.IsMaximal.outproof · cited by 16
Cited by11
Results whose statement or proof uses this declaration.
- Ideal.IsMaximal.ne_topproof · cited by 42
- RingOfIntegers.not_dvd_exponent_iffproof · cited by 4
- Ideal.ramificationIdx_eq_one_iffproof · cited by 4
- Ideal.isCoprime_of_isMaximalproof · cited by 3
- Ideal.ramificationIdx_eq_oneproof · cited by 3
- ContinuousMap.idealOfSet_isMaximal_iffproof · cited by 2
- Ideal.mem_primesOver_iff_mem_normalizedFactorsproof · cited by 2
- Ideal.under_map_eq_map_underproof · cited by 1
- Ideal.liesOver_iff_dvd_mapproof · cited by 1
- Ring.DimensionLEOne.localizationproof · cited by 1
- IsSimpleModule.ker_toSpanSingleton_isMaximalproof · cited by 1