Theorems · Theorem · commutative algebra
Ideal.span_le
∀ {α : Type u} [inst : Semiring α] {s : Set α} {I : Ideal α}, Ideal.span s ≤ I ↔ s ⊆ ↑I- Defined in
- Mathlib.RingTheory.Ideal.Span
- Cited by
- 70 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- SetLike.coestatement · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Ideal.spanstatement · cited by 948
- Submodule.span_leproof · cited by 164
Cited by70
Results whose statement or proof uses this declaration.
- Ideal.map_le_iff_le_comapproof · cited by 60
- Ideal.map_spanproof · cited by 43
- Ideal.span_singleton_le_span_singletonproof · cited by 15
- Ideal.map_mulproof · cited by 9
- PadicInt.maximalIdeal_eq_span_pproof · cited by 6
- Ideal.height_le_spanRank_toENat_of_mem_minimalPrimesproof · cited by 5
- Ideal.dvd_span_singletonproof · cited by 5
- Ideal.spanNorm_singletonproof · cited by 5
- Ideal.exists_radical_pow_le_of_fgproof · cited by 4
- Ideal.span_pow_eq_topproof · cited by 4
- DividedPowers.span_isSubDPIdeal_iffproof · cited by 3
- Ideal.homogeneousCore'_leproof · cited by 3