Theorems · Theorem · commutative algebra
ringKrullDim_le_of_surjective
∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring S] (f : R →+* S),
Function.Surjective ⇑f → ringKrullDim S ≤ ringKrullDim RIf f : R →+* S is surjective, then ringKrullDim S ≤ ringKrullDim R.
- Defined in
- Mathlib.RingTheory.KrullDimension.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 35 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- ENatstatement · cited by 4,985
- WithBotstatement · cited by 1,498
- PrimeSpectrumproof · cited by 625
- Ideal.comapproof · cited by 443
- PrimeSpectrum.asIdealproof · cited by 333
- ringKrullDimstatement · cited by 75
- Ideal.comap_monoproof · cited by 25
- Monotone.strictMono_of_injectiveproof · cited by 22
- Ideal.comap_injective_of_surjectiveproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- ringKrullDim_eq_of_ringEquivproof · cited by 9
- ringKrullDim_succ_le_of_surjectiveproof · cited by 2
- ringKrullDim_add_enatCard_le_ringKrullDim_mvPolynomialproof · cited by 0
- ringKrullDim_quotient_leproof · cited by 0