Theorems · Theorem · commutative algebra
IsLocalRing.le_maximalIdeal_of_isPrime
∀ {R : Type u_1} [inst : CommSemiring R] [inst_1 : IsLocalRing R] (p : Ideal R) [hp : p.IsPrime],
p ≤ IsLocalRing.maximalIdeal R- Cited by
- 3 results in Mathlib
- Foundations
- Depth 76 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.IsPrimestatement and proof · cited by 827
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement · cited by 297
- Ideal.IsPrime.ne_topproof · cited by 82
- IsLocalRing.le_maximalIdealproof · cited by 20
Cited by3
Results whose statement or proof uses this declaration.
- PrimeSpectrum.exist_mem_one_of_mem_maximal_idealproof · cited by 1
- Algebra.QuasiFiniteAt.eq_of_le_of_under_eqproof · cited by 1
- ringKrullDim_natproof · cited by 0