Theorems · Theorem · commutative algebra
KaehlerDifferential.span_range_derivation
∀ (R : Type u) (S : Type v) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S], Submodule.span S (Set.range ⇑(KaehlerDifferential.D R S)) = ⊤
- Defined in
- Mathlib.RingTheory.Kaehler.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 97 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
- Top.topstatement and proof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Set.rangestatement and proof · cited by 4,705
- TensorProductproof · cited by 2,545
- Submodule.spanstatement and proof · cited by 1,504
- TensorProduct.tmulproof · cited by 1,182
- Derivationstatement · cited by 293
- eq_top_iffproof · cited by 236
- Submodule.subset_spanproof · cited by 234
Cited by7
Results whose statement or proof uses this declaration.
- Derivation.liftKaehlerDifferential_uniqueproof · cited by 5
- KaehlerDifferential.linearCombination_surjectiveproof · cited by 3
- KaehlerDifferential.span_range_map_derivation_of_isLocalizationproof · cited by 1
- KaehlerDifferential.map_surjective_of_surjectiveproof · cited by 1
- KaehlerDifferential.subsingleton_of_surjectiveproof · cited by 1
- CommRingCat.KaehlerDifferential.extproof · cited by 1
- Algebra.Extension.tensorCotangentSpace_tmul_tmulproof · cited by 1