Theorems · Theorem · commutative algebra
Algebra.Presentation.quotientEquiv_symm
∀ {R : Type u} {S : Type v} {ι : Type w} {σ : Type t} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
(P : Algebra.Presentation R S ι σ) (x : S), P.quotientEquiv.symm x = (Ideal.Quotient.mk P.ker) (P.σ x)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- Idealstatement · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- AlgEquivstatement · cited by 1,681
- AlgEquiv.symmstatement · cited by 615
- Ideal.Quotient.mkstatement · cited by 610
- Algebra.Generators.Ringstatement · cited by 133
- Algebra.Presentation.toGeneratorsstatement · cited by 104
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