Theorems · Theorem · commutative algebra
Ideal.span_mono
∀ {α : Type u} [inst : Semiring α] {s t : Set α}, s ⊆ t → Ideal.span s ≤ Ideal.span t- Defined in
- Mathlib.RingTheory.Ideal.Span
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, 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_monoproof · cited by 85
Cited by16
Results whose statement or proof uses this declaration.
- Ideal.map_monoproof · cited by 29
- Ideal.span_eq_top_iff_finiteproof · cited by 10
- Ideal.homogeneousCore'_monoproof · cited by 1
- Ideal.homogeneousHull_monoproof · cited by 1
- Localization.existsUnique_algebraMap_eq_of_span_eq_topproof · cited by 1
- IsGCDMonoid.isPrincipal_of_exists_mul_ne_zero_isPrincipalproof · cited by 1
- Ideal.le_spanNorm_spanNormproof · cited by 1
- Ideal.spanNorm_monoproof · cited by 1
- AlgebraicGeometry.eq_top_of_sigmaSpec_subset_of_isCompactproof · cited by 1
- Ideal.spanNorm_mul_spanNorm_leproof · cited by 1
- DividedPowers.isSubDPIdeal_iSupproof · cited by 0