Theorems · Theorem · commutative algebra
Ring.DimensionLEOne.maximalOfPrime
∀ {R : Type u_1} {inst : CommRing R} [self : Ring.DimensionLEOne R] {p : Ideal R}, p ≠ ⊥ → p.IsPrime → p.IsMaximal- Defined in
- Mathlib.RingTheory.DedekindDomain.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- Ring.DimensionLEOne
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.
- CommRingstatement and proof · cited by 17,173
- Idealstatement · cited by 4,748
- Bot.botstatement · cited by 4,720
- Ideal.IsPrimestatement · cited by 827
- Ideal.IsMaximalstatement · cited by 452
- Ring.DimensionLEOnestatement and proof · cited by 12
Cited by6
Results whose statement or proof uses this declaration.
- Ideal.IsPrime.isMaximalproof · cited by 24
- Ideal.ramificationIdx'_algebra_towerproof · cited by 2
- Ideal.absNorm_relNormproof · cited by 2
- Ring.DimensionLEOne.of_ringEquivproof · cited by 0
- IsDedekindDomain.primesOverEquivPrimesOver_inertiagDeg_eqproof · cited by 0
- NumberField.torsionOrder_dvd_absNorm_sub_oneproof · cited by 0