Theorems · Theorem · commutative algebra
Ideal.IsMaximal.lt_top
∀ {α : Type u} [inst : Semiring α] {I : Ideal α}, I.IsMaximal → I < ⊤- Defined in
- Mathlib.RingTheory.Ideal.Maximal
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Top.topstatement · cited by 9,680
- Idealstatement and proof · cited by 4,748
- Ideal.IsMaximalstatement and proof · cited by 452
- Ne.lt_topproof · cited by 161
- Ideal.IsMaximal.ne_topproof · cited by 42
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.ramificationIdx_posproof · cited by 5
- IsLocalRing.map_maximalIdeal_lt_topproof · cited by 1
- FractionalIdeal.isPrincipal.of_finite_maximals_of_invproof · cited by 1