Theorems · Theorem · field theory
RatFunc.liftMonoidWithZeroHom_apply_ofFractionRing_mk
∀ {G₀ : Type u_1} {R : Type u_3} [inst : CommGroupWithZero G₀] [inst_1 : CommRing R] (φ : Polynomial R →*₀ G₀)
(hφ : nonZeroDivisors (Polynomial R) ≤ Submonoid.comap φ (nonZeroDivisors G₀)) (n : Polynomial R)
(d : ↥(nonZeroDivisors (Polynomial R))),
(RatFunc.liftMonoidWithZeroHom φ hφ) { toFractionRing := Localization.mk n d } = φ n / φ ↑d- Defined in
- Mathlib.FieldTheory.RatFunc.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommGroupWithZeroCommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Submonoidstatement · cited by 3,086
- nonZeroDivisorsstatement and proof · cited by 895
- MonoidWithZeroHomstatement and proof · cited by 704
- RatFuncstatement · cited by 301
- Submonoid.comapstatement and proof · cited by 179
- Localization.mkstatement · cited by 110
- CommGroupWithZerostatement and proof · cited by 94
- RatFunc.liftMonoidWithZeroHomstatement · cited by 6
- RatFunc.liftOn_ofFractionRing_mkproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- RatFunc.liftMonoidWithZeroHom_apply_divproof · cited by 4
- RatFunc.liftMonoidWithZeroHom_injectiveproof · cited by 2
- RatFunc.liftRingHom_apply_ofFractionRing_mkproof · cited by 1
- RatFunc.liftAlgHom_apply_ofFractionRing_mkproof · cited by 0