Theorems · Theorem · commutative algebra
Ideal.IsMaximal.coprime_of_ne
∀ {α : Type u} [inst : Semiring α] {M M' : Ideal α}, M.IsMaximal → M'.IsMaximal → M ≠ M' → M ⊔ M' = ⊤- Defined in
- Mathlib.RingTheory.Ideal.Maximal
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 64 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
- Idealstatement and proof · cited by 4,748
- Ideal.IsMaximalstatement and proof · cited by 452
- LE.le.trans_eqproof · cited by 328
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- Ideal.IsMaximal.ne_topproof · cited by 42
- Ideal.IsMaximal.eq_of_leproof · cited by 39
Cited by5
Results whose statement or proof uses this declaration.
- Ideal.eq_prime_pow_mul_coprimeproof · cited by 3
- IsDedekindDomain.inf_pow_eq_prod_of_primeproof · cited by 3
- IsDedekindDomain.HeightOneSpectrum.isCoprime_of_neproof · cited by 1
- MaximalSpectrum.isCoprime_of_neproof · cited by 1
- FractionalIdeal.isPrincipal.of_finite_maximals_of_invproof · cited by 1