Theorems · Theorem · commutative algebra
Ideal.span_union
∀ {α : Type u} [inst : Semiring α] (s t : Set α), Ideal.span (s ∪ t) = Ideal.span s ⊔ Ideal.span t- Defined in
- Mathlib.RingTheory.Ideal.Span
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 65 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Idealstatement · cited by 4,748
- Ideal.spanstatement · cited by 948
- Submodule.span_unionproof · cited by 23
Cited by11
Results whose statement or proof uses this declaration.
- IsRelPrime.isCoprimeproof · cited by 5
- Ideal.height_le_spanRank_toENat_of_mem_minimalPrimesproof · cited by 5
- Ideal.height_le_height_add_spanFinrank_of_leproof · cited by 2
- NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply_eq_spanproof · cited by 2
- PrimeSpectrum.exists_mul_eq_zero_add_eq_one_basicOpen_eq_of_isClopenproof · cited by 2
- Ideal.ofList_appendproof · cited by 1
- Ideal.isOka_fgproof · cited by 1
- Algebra.Presentation.span_range_relation_eq_ker_compproof · cited by 0
- DividedPowers.isSubDPIdeal_supproof · cited by 0