Theorems · Theorem · commutative algebra
Algebra.Presentation.relation_mem_ker
∀ {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) (i : σ), P.relation i ∈ P.ker- Cited by
- 9 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Algebrastatement and proof · cited by 11,388
- Finsuppstatement · cited by 5,255
- Idealstatement and proof · cited by 4,748
- Algebra.Generators.Ringstatement and proof · cited by 133
- Algebra.Presentation.toGeneratorsstatement and proof · cited by 104
- Ideal.subset_spanproof · cited by 86
- Algebra.Presentationstatement and proof · cited by 70
- Algebra.Presentation.relationstatement and proof · cited by 49
- Algebra.Generators.kerstatement · cited by 46
- Algebra.Presentation.span_range_relation_eq_kerproof · cited by 10
Cited by9
Results whose statement or proof uses this declaration.
- Algebra.Generators.exists_presentation_of_basis_cotangentstatement and proof · cited by 2
- Algebra.SubmersivePresentation.basisCotangent_applystatement and proof · cited by 2
- Algebra.IsStandardSmooth.of_basis_kaehlerDifferentialproof · cited by 2
- Algebra.SubmersivePresentation.cotangentComplexAux_injectiveproof · cited by 1
- Algebra.Generators.C_mul_X_sub_one_mem_kerproof · cited by 1
- Algebra.PreSubmersivePresentation.isUnit_jacobian_of_cotangentRestrict_bijectivestatement and proof · cited by 1
- Algebra.SubmersivePresentation.cotangentComplexAux_surjectiveproof · cited by 0
- Algebra.Generators.exists_presentation_of_free_cotangentstatement and proof · cited by 0
- Algebra.Presentation.mem_ker_naiveproof · cited by 0