Theorems · Theorem · commutative algebra
Ideal.isMaximal_of_isPrime
∀ {R : Type u_1} [inst : CommSemiring R] [Ring.KrullDimLE 0 R] (I : Ideal R) [I.IsPrime], I.IsMaximal- Defined in
- Mathlib.RingTheory.KrullDimension.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.IsPrimestatement and proof · cited by 827
- Ideal.IsMaximalstatement · cited by 452
- Ring.KrullDimLEstatement and proof · cited by 79
- Ring.krullDimLE_zero_iffproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.IsPrime.isMaximal'proof · cited by 2