Theorems · Theorem · commutative algebra
DividedPowers.dpow_span_isSubideal
∀ {A : Type u_1} [inst : CommSemiring A] {I : Ideal A} (hI : DividedPowers I) {S : Set A},
S ⊆ ↑I → Ideal.span {y | ∃ n, ∃ (_ : n ≠ 0), ∃ x, ∃ (_ : x ∈ S), y = hI.dpow n x} ≤ I- Cited by
- 2 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Set.ofPredstatement and proof · cited by 6,101
- Idealstatement and proof · cited by 4,748
- Ideal.spanstatement · cited by 948
- DividedPowersstatement and proof · cited by 112
- DividedPowers.dpowstatement and proof · cited by 85
- Ideal.span_leproof · cited by 70
- DividedPowers.dpow_memproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- DividedPowers.SubDPIdeal.dpow_mem_span_of_mem_spanproof · cited by 1
- DividedPowers.SubDPIdeal.span_carrier_eq_dpow_spanproof · cited by 0