Theorems · Theorem · commutative algebra
Submodule.pow_succ
∀ {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}, M ^ (n + 1) = M ^ n * M- Defined in
- Mathlib.Algebra.Algebra.Operations
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
Cited by6
Results whose statement or proof uses this declaration.
- Submodule.pow_oneproof · cited by 6
- Ideal.pow_right_monoproof · cited by 5
- IsSemiprimaryRing.inductionproof · cited by 2
- Ideal.top_powproof · cited by 2
- Ideal.sup_pow_eq_topproof · cited by 2
- Submodule.pow_toAddSubmonoidproof · cited by 1