Theorems · Theorem · field theory
RatFunc.mk_eq_localization_mk
∀ {K : Type u} [inst : CommRing K] [inst_1 : IsDomain K] (p : Polynomial K) {q : Polynomial K} (hq : q ≠ 0),
RatFunc.mk p q = { toFractionRing := Localization.mk p ⟨q, ⋯⟩ }- Defined in
- Mathlib.FieldTheory.RatFunc.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Submonoidstatement · cited by 3,086
- IsDomainstatement and proof · cited by 2,196
- nonZeroDivisorsstatement and proof · cited by 895
- RatFuncstatement and proof · cited by 301
- Localizationproof · cited by 270
- IsLocalization.mk'proof · cited by 218
- FractionRingproof · cited by 200
- Localization.mkstatement and proof · cited by 110
- mem_nonZeroDivisors_iff_ne_zerostatement and proof · cited by 38
- Localization.mk_eq_mk'proof · cited by 25
Cited by4
Results whose statement or proof uses this declaration.
- RatFunc.liftMonoidWithZeroHom_apply_divproof · cited by 4
- RatFunc.map_apply_div_ne_zeroproof · cited by 2
- RatFunc.liftOn_mkproof · cited by 2
- RatFunc.mk_smulproof · cited by 1