Theorems · Theorem · commutative algebra
Ideal.span_singleton_abs
∀ {α : Type u} [inst : Ring α] (x : α) [inst_1 : LinearOrder α], Ideal.span {|x|} = Ideal.span {x}- Defined in
- Mathlib.RingTheory.Ideal.Span
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
- Assumes
- RingLinearOrder
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
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- Idealstatement · cited by 4,748
- absstatement and proof · cited by 1,814
- Ideal.spanstatement and proof · cited by 948
- abs_choiceproof · cited by 16
- Ideal.span_singleton_negproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Int.ideal_span_absNorm_eq_selfproof · cited by 4
- NumberField.exists_not_isUnramifiedInproof · cited by 1
- Ideal.span_insert_absproof · cited by 1
- Rat.HeightOneSpectrum.span_natGeneratorproof · cited by 1