Theorems · Theorem · commutative algebra
Ideal.span_singleton_one
∀ {α : Type u} [inst : Semiring α], Ideal.span {1} = ⊤- Defined in
- Mathlib.RingTheory.Ideal.Span
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Top.topstatement · cited by 9,680
- Idealstatement · cited by 4,748
- Ideal.spanstatement and proof · cited by 948
- Set.mem_singletonproof · cited by 183
- Ideal.subset_spanproof · cited by 86
- Ideal.eq_top_iff_oneproof · cited by 56
Cited by21
Results whose statement or proof uses this declaration.
- Ideal.one_eq_topproof · cited by 83
- Ideal.span_singleton_eq_topproof · cited by 10
- FractionalIdeal.count_oneproof · cited by 4
- FractionalIdeal.count_selfproof · cited by 3
- Ideal.multiset_prod_span_singletonproof · cited by 2
- ClassGroup.mk_eq_one_of_coe_idealproof · cited by 2
- Ideal.span_oneproof · cited by 2
- FractionalIdeal.count_maximal_coprimeproof · cited by 2
- RingHom.locally_ofproof · cited by 2
- Algebra.Generators.exists_presentation_of_basis_cotangentproof · cited by 2
- FractionalIdeal.count_coeproof · cited by 1
- Ideal.Quotient.span_singleton_oneproof · cited by 1