Theorems · Theorem · commutative algebra
Algebra.PreSubmersivePresentation.localizationAway_jacobiMatrix
∀ {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.PreSubmersivePresentation.localizationAway S r).jacobiMatrix = Matrix.diagonal fun x => MvPolynomial.C r- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Finsuppstatement · cited by 5,255
- Matrixstatement · cited by 4,303
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- MvPolynomialstatement · cited by 2,140
- MulZeroClass.mul_zeroproof · cited by 2,091
- sub_zeroproof · cited by 938
- map_subproof · cited by 565
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.PreSubmersivePresentation.localizationAway_jacobianproof · cited by 0