Theorems · Theorem · commutative algebra
IsLocalRing.CotangentSpace.map_eq_top_iff
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsLocalRing R] [IsNoetherianRing R]
{M : Submodule R ↥(IsLocalRing.maximalIdeal R)}, Submodule.map (IsLocalRing.maximalIdeal R).toCotangent M = ⊤ ↔ M = ⊤- Defined in
- Mathlib.RingTheory.Ideal.Cotangent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Top.topstatement and proof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- le_reflproof · cited by 2,061
- LinearMap.kerproof · cited by 848
- Submodule.mapstatement and proof · cited by 614
- Submodule.subtypeproof · cited by 480
- Eq.geproof · cited by 375
- smul_eq_mulproof · cited by 357
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalRing.CotangentSpace.span_image_eq_top_iffproof · cited by 0