Theorems · Theorem · commutative algebra
Ideal.pow_eq_top_iff
∀ {R : Type u} [inst : Semiring R] {I : Ideal R} {n : ℕ}, I ^ n = ⊤ ↔ I = ⊤ ∨ n = 0- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 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.
Cites9
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
- Top.topstatement and proof · cited by 9,680
- Submoduleproof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- Ideal.one_eq_topproof · cited by 83
- Ideal.eq_top_iff_oneproof · cited by 56
- Ideal.pow_le_selfproof · cited by 16
- Submodule.pow_zeroproof · cited by 9
- Ideal.top_powproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.Quotient.isUnit_mk_pow_of_notMemproof · cited by 0