Theorems · Theorem · commutative algebra
Ideal.sup_pow_eq_top
∀ {R : Type u} [inst : Semiring R] {I J : Ideal R} [I.IsTwoSided] {n : ℕ}, I ⊔ J = ⊤ → I ⊔ J ^ n = ⊤- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringIdeal.IsTwoSided
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.IsTwoSidedstatement and proof · cited by 179
- sup_of_le_rightproof · cited by 143
- Ideal.one_eq_topproof · cited by 83
- Submodule.pow_succproof · cited by 6
- Ideal.sup_mul_eq_of_coprime_leftproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.pow_sup_pow_eq_topproof · cited by 2
- Ideal.pow_sup_eq_top'proof · cited by 1