Theorems · Theorem · commutative algebra
Ideal.span_mul_span
∀ {R : Type u} [inst : Semiring R] (S T : Set R) [(Ideal.span S).IsTwoSided],
Ideal.span S * Ideal.span T = Ideal.span (S * T)- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringIdeal.IsTwoSided
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 and proof · cited by 948
- Set.mulstatement · cited by 297
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Submodule.span_smul_spanproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Ideal.map_mulproof · cited by 9
- Ideal.span_mul_span'proof · cited by 4
- IsGCDMonoid.isPrincipal_of_exists_mul_ne_zero_isPrincipalproof · cited by 1
- Algebra.IsLocalIso.transproof · cited by 1
- AlgebraicGeometry.Scheme.zeroLocus_mulproof · cited by 0