Theorems · Theorem · commutative algebra
DividedPowers.span_isSubDPIdeal_iff
∀ {A : Type u_1} [inst : CommSemiring A] {I : Ideal A} {hI : DividedPowers I} {S : Set A},
S ⊆ ↑I → (hI.IsSubDPIdeal (Ideal.span S) ↔ ∀ {n : ℕ}, n ≠ 0 → ∀ s ∈ S, hI.dpow n s ∈ Ideal.span S)[P. Berthelot and A. Ogus, Notes on crystalline cohomology (Lemma 3.6)][BerthelotOgus-1978]
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Idealstatement and proof · cited by 4,748
- Submodule.spanproof · cited by 1,504
- Finset.rangeproof · cited by 1,341
- Ideal.spanstatement and proof · cited by 948
- smul_eq_mulproof · cited by 357
- DividedPowersstatement and proof · cited by 112
- Ideal.mul_mem_leftproof · cited by 107
- Ideal.subset_spanproof · cited by 86
- DividedPowers.dpowstatement and proof · cited by 85
Cited by3
Results whose statement or proof uses this declaration.
- DividedPowers.isSubDPIdeal_map_of_isSubDPIdealproof · cited by 1
- DividedPowers.isSubDPIdeal_supproof · cited by 0
- DividedPowers.isSubDPIdeal_iSupproof · cited by 0