Theorems · Theorem · commutative algebra
Ideal.IsMaximal.ne_bot_of_isIntegral_int
∀ {R : Type u_1} [inst : CommRing R] [CharZero R] [Algebra.IsIntegral ℤ R] (I : Ideal R) [I.IsMaximal], I ≠ ⊥- Cited by
- 2 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- Bot.botstatement · cited by 4,720
- CharZerostatement and proof · cited by 932
- Ideal.IsMaximalstatement and proof · cited by 452
- Algebra.IsIntegralstatement and proof · cited by 224
- FaithfulSMul.algebraMap_injectiveproof · cited by 198
- IsFieldproof · cited by 103
- Ring.ne_bot_of_isMaximal_of_not_isFieldproof · cited by 8
- isField_of_isIntegral_of_isFieldproof · cited by 4
- Int.not_isFieldproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.exists_prime_and_absNorm_eq_powproof · cited by 1
- NumberField.exists_not_isUnramifiedAt_int_of_isGaloisproof · cited by 0