Theorems · Theorem · commutative algebra
Ideal.sup_mul_eq_of_coprime_left
∀ {R : Type u} [inst : Semiring R] {I J K : Ideal R} [I.IsTwoSided], I ⊔ J = ⊤ → I ⊔ J * K = I ⊔ K- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 72 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.
Cites15
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
- one_mulproof · cited by 2,841
- le_antisymmproof · cited by 2,068
- add_assocproof · cited by 746
- add_mulproof · cited by 363
- AddMemClass.add_memproof · cited by 229
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Submodule.mem_supproof · cited by 73
- Ideal.mul_mem_rightproof · cited by 71
- Ideal.eq_top_iff_oneproof · cited by 56
Cited by4
Results whose statement or proof uses this declaration.
- Ideal.sup_pow_eq_topproof · cited by 2
- Ideal.sup_multiset_prod_eq_topproof · cited by 1
- Ideal.sup_prod_eq_topproof · cited by 1
- Ideal.mul_sup_eq_of_coprime_leftproof · cited by 0