Theorems · Theorem · commutative algebra
Ideal.isCoprime_of_isMaximal
∀ {R : Type u} [inst : CommSemiring R] {I J : Ideal R} [I.IsMaximal] [J.IsMaximal], I ≠ J → IsCoprime I J- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- Ideal.IsMaximalstatement and proof · cited by 452
- IsCoprimestatement · cited by 321
- Ideal.isMaximal_defproof · cited by 11
- Ideal.isCoprime_iff_codisjointproof · cited by 6
- IsCoatom.codisjoint_of_neproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- IsNoetherianRing.isArtinianRing_of_krullDimLE_zeroproof · cited by 2
- Module.nonempty_basis_of_flat_of_finrank_eqproof · cited by 1
- IsLocalRing.exists_surjective_of_not_isLocalRingproof · cited by 0