Theorems · Theorem · commutative algebra
Ideal.add_eq_one_iff
∀ {R : Type u} [inst : Semiring R] {I J : Ideal R}, I + J = 1 ↔ ∃ i ∈ I, ∃ j ∈ J, i + j = 1- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, 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
- Idealstatement and proof · cited by 4,748
- Ideal.one_eq_topproof · cited by 83
- Submodule.mem_supproof · cited by 73
- Ideal.eq_top_iff_oneproof · cited by 56
- Ideal.add_eq_supproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.isCoprime_iff_existsproof · cited by 4
- Algebra.exists_aeval_invOf_eq_zero_of_idealMap_adjoin_sup_span_eq_topproof · cited by 3