Theorems · Theorem · commutative algebra
Submodule.pow_toAddSubmonoid
∀ {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) {n : ℕ}, n ≠ 0 → (M ^ n).toAddSubmonoid = M.toAddSubmonoid ^ n- Defined in
- Mathlib.Algebra.Algebra.Operations
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- one_mulproof · cited by 2,841
- AddSubmonoidstatement and proof · cited by 1,178
- pow_zeroproof · cited by 1,094
- pow_succproof · cited by 374
- Submodule.toAddSubmonoidstatement and proof · cited by 162
- Submodule.pow_zeroproof · cited by 9
- Submodule.pow_succproof · cited by 6
- AddSubmonoid.monoidstatement · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.le_pow_toAddSubmonoidproof · cited by 1