Theorems · Theorem · commutative algebra
ringKrullDim_eq_of_ringEquiv
∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring S] (e : R ≃+* S),
ringKrullDim R = ringKrullDim SIf R and S are isomorphic, then ringKrullDim R = ringKrullDim S.
- Defined in
- Mathlib.RingTheory.KrullDimension.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- ENatstatement · cited by 4,985
- le_antisymmproof · cited by 2,068
- WithBotstatement · cited by 1,498
- RingEquivstatement and proof · cited by 1,147
- RingHomClass.toRingHomproof · cited by 746
- RingEquiv.symmproof · cited by 567
- ringKrullDimstatement · cited by 75
- RingEquiv.surjectiveproof · cited by 28
- ringKrullDim_le_of_surjectiveproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- IsRegularLocalRing.of_ringEquivproof · cited by 2
- ringKrullDim_mvPolynomial_of_isEmptyproof · cited by 2
- ringKrullDim_add_natCard_le_ringKrullDim_mvPolynomialproof · cited by 1
- RingEquiv.ringKrullDimproof · cited by 1
- IsLocalization.height_map_of_disjointproof · cited by 1
- MvPolynomial.ringKrullDim_of_isNoetherianRingproof · cited by 0
- ringKrullDim_add_length_eq_ringKrullDim_of_isRegularproof · cited by 0
- Polynomial.ringKrullDim_leproof · cited by 0