Theorems · Theorem · commutative algebra
Algebra.Extension.Cotangent.finite
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
{P : Algebra.Extension R S}, P.ker.FG → Module.Finite S P.Cotangent- Defined in
- Mathlib.RingTheory.Extension.Basic
- Cited by
- 1 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.
Cites18
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
- Submoduleproof · cited by 7,192
- Module.Finitestatement · cited by 1,032
- Submodule.FGproof · cited by 230
- Algebra.Extension.Ringstatement and proof · cited by 179
- Algebra.Extensionstatement and proof · cited by 138
- Algebra.Extension.Cotangentstatement and proof · cited by 121
- LinearMap.range_eq_topproof · cited by 107
- Submodule.map_topproof · cited by 105
- Ideal.FGstatement and proof · cited by 99
- Algebra.Extension.kerstatement and proof · cited by 72
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.Generators.exists_presentation_of_free_cotangentproof · cited by 0