Theorems · Theorem · commutative algebra
Submodule.pow_mem_pow
∀ {R : Type u} [inst : Semiring R] {A : Type v} [inst_1 : Semiring A] [inst_2 : Module R A]
[inst_3 : IsScalarTower R A A] (M : Submodule R A) {x : A}, x ∈ M → ∀ (n : ℕ), x ^ n ∈ M ^ 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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- Submodulestatement and proof · cited by 7,192
- IsScalarTowerstatement and proof · cited by 3,896
- Submodule.pow_subset_powproof · cited by 2
- Set.pow_mem_powproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.pow_mem_powproof · cited by 19
- MvPolynomial.monomial_mem_homogeneousSubmodule_pow_degreeproof · cited by 1
- Polynomial.coeff_modByMonic_mem_pow_natDegree_mulproof · cited by 0