Theorems · Theorem · commutative algebra
Ideal.span_range_pow_eq_top
∀ {α : Type u_2} [inst : CommSemiring α] (s : Set α),
Ideal.span s = ⊤ → ∀ (n : ↑s → ℕ), Ideal.span (Set.range fun x => ↑x ^ n x) = ⊤- Defined in
- Mathlib.RingTheory.Ideal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 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.
Cites25
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
- Finsetproof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Set.Elemstatement and proof · cited by 7,166
- Set.imageproof · cited by 5,609
- Idealstatement · cited by 4,748
- Set.rangestatement and proof · cited by 4,705
- LE.le.transproof · cited by 3,151
- Submodule.spanproof · cited by 1,504
- Ideal.spanstatement and proof · cited by 948
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.mem_of_span_eq_top_of_smul_pow_memproof · cited by 6