Theorems · Theorem · commutative algebra
Submodule.span_pow
∀ {R : Type u} [inst : CommSemiring R] {A : Type v} [inst_1 : Semiring A] [inst_2 : Algebra R A] (s : Set A) (n : ℕ),
Submodule.span R s ^ n = Submodule.span R (s ^ n)- Defined in
- Mathlib.Algebra.Algebra.Operations
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement · cited by 7,192
- Submodule.spanstatement · cited by 1,504
- Set.NPowstatement · cited by 51
Cited by3
Results whose statement or proof uses this declaration.
- exteriorPower.ιMulti_span_fixedDegree_of_span_eq_topproof · cited by 2
- Submodule.pow_eq_span_pow_setproof · cited by 1
- MvPolynomial.pow_idealOfVars_eq_spanproof · cited by 0