Theorems · Theorem · commutative algebra
exists_max_ideal_of_mem_nonunits
∀ {α : Type u_2} {a : α} [inst : CommSemiring α], a ∈ nonunits α → ∃ I, I.IsMaximal ∧ a ∈ I- Defined in
- Mathlib.RingTheory.Ideal.Nonunits
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Top.topproof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- Ideal.spanproof · cited by 948
- Ideal.IsMaximalstatement and proof · cited by 452
- Set.mem_singletonproof · cited by 183
- Ideal.subset_spanproof · cited by 86
- Ideal.exists_le_maximalproof · cited by 47
- nonunitsstatement and proof · cited by 35
- Ideal.span_singleton_eq_topproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- IsLocalRing.of_unique_max_idealproof · cited by 4
- TrivSqZeroExt.isUnit_or_isNilpotent_of_isMaximal_isNilpotentproof · cited by 0
- IsLocalHom.of_comap_surjectiveproof · cited by 0