Theorems · Theorem · commutative algebra
Submodule.pow_eq_bot
∀ {R : Type u} [inst : Semiring R] {A : Type v} [inst_1 : Semiring A] [inst_2 : Module R A]
[inst_3 : IsScalarTower R A A] [IsReduced A] {M : Submodule R A} {n : ℕ}, n ≠ 0 → (M ^ n = ⊥ ↔ M = ⊥)- Defined in
- Mathlib.Algebra.Algebra.Operations
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Bot.botstatement and proof · cited by 4,720
- IsScalarTowerstatement and proof · cited by 3,896
- IsReducedstatement and proof · cited by 98
- eq_zero_of_pow_eq_zeroproof · cited by 30
- Submodule.bot_powproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.pow_eq_botproof · cited by 0