Theorems · Theorem · commutative algebra
isNoetherianRing_of_ringEquiv
∀ (R : Type u_1) [inst : Semiring R] {S : Type u_2} [inst_1 : Semiring S] (f : R ≃+* S) [IsNoetherianRing R],
IsNoetherianRing S- Defined in
- Mathlib.RingTheory.Noetherian.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 85 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.
- Semiringstatement and proof · cited by 13,802
- RingEquivstatement and proof · cited by 1,147
- IsNoetherianRingstatement and proof · cited by 268
- Equiv.surjectiveproof · cited by 198
- RingEquiv.toRingHomproof · cited by 150
- RingEquiv.toEquivproof · cited by 101
- isNoetherianRing_of_surjectiveproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- IsRegularLocalRing.of_ringEquivproof · cited by 2
- AlgebraicGeometry.isLocallyNoetherian_iff_of_affine_openCoverproof · cited by 2
- AlgebraicGeometry.isLocallyNoetherian_iff_openCoverproof · cited by 2
- AlgebraicGeometry.isLocallyNoetherian_of_affine_coverproof · cited by 2
- MvPolynomial.isNoetherianRing_fin_0proof · cited by 0
- AlgebraicGeometry.isLocallyNoetherian_Specproof · cited by 0
- IsRegularRing.of_ringEquivproof · cited by 0
- AlgebraicGeometry.noetherianSpace_of_isAffineOpenproof · cited by 0