Theorems · Theorem · commutative algebra
Algebra.Generators.ker_localizationAway
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (r : R)
[inst_3 : IsLocalization.Away r S],
(Algebra.Generators.localizationAway S r).ker = Ideal.span {MvPolynomial.C r * MvPolynomial.X () - 1}- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
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
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- Finsuppstatement · cited by 5,255
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- AlgHomproof · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- Ideal.spanstatement and proof · cited by 948
- RingHomClass.toRingHomproof · cited by 746
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.Generators.comp_localizationAway_kerproof · cited by 1