Theorems · Theorem · commutative algebra
Ideal.pow_eq_zero_of_mem
∀ {R : Type u} [inst : Semiring R] {I : Ideal R} {n m : ℕ}, I ^ n = 0 → n ≤ m → ∀ {x : R}, x ∈ I → x ^ m = 0- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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.
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- Ideal.pow_le_pow_rightproof · cited by 39
- Ideal.pow_mem_powproof · cited by 19
Cited by5
Results whose statement or proof uses this declaration.
- DividedPowers.IsNilpotent.dpow_of_prime_leproof · cited by 0
- DividedPowers.OfInvertibleFactorial.dpow_compproof · cited by 0
- DividedPowers.CharP.dpow_of_prime_leproof · cited by 0
- DividedPowers.OfInvertibleFactorial.mul_dpowproof · cited by 0
- DividedPowers.OfSquareZero.dpow_of_two_leproof · cited by 0