Theorems · Theorem · commutative algebra
Ideal.mul_sup_eq_of_coprime_left
∀ {R : Type u} [inst : Semiring R] {I J K : Ideal R} [J.IsTwoSided], I ⊔ J = ⊤ → I * K ⊔ J = K ⊔ J- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringIdeal.IsTwoSided
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Cites6
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
- Idealstatement and proof · cited by 4,748
- Ideal.IsTwoSidedstatement and proof · cited by 179
- sup_commproof · cited by 165
- Ideal.sup_mul_eq_of_coprime_leftproof · cited by 4
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