Theorems · Theorem · commutative algebra
Algebra.pow_smul_mem_adjoin_smul
∀ {R : Type uR} {A : Type uA} [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : Algebra R A] (r : R)
(s : Set A) {x : A}, x ∈ Algebra.adjoin R s → ∃ n₀, ∀ n ≥ n₀, r ^ n • x ∈ Algebra.adjoin R (r • s)- Defined in
- Mathlib.RingTheory.Adjoin.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Subalgebrastatement · cited by 1,353
- Set.smulSetstatement · cited by 608
- Algebra.adjoinstatement and proof · cited by 535
- Algebra.subset_adjoinproof · cited by 109
- Subalgebra.algebraMap_memproof · cited by 28
- Algebra.pow_smul_mem_of_smul_subset_of_mem_adjoinproof · cited by 2
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