Theorems · Theorem · commutative algebra
IsLocalRing.CotangentSpace.span_image_eq_top_iff
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsLocalRing R] [IsNoetherianRing R]
{s : Set ↥(IsLocalRing.maximalIdeal R)},
Submodule.span (IsLocalRing.ResidueField R) (⇑(IsLocalRing.maximalIdeal R).toCotangent '' s) = ⊤ ↔
Submodule.span R s = ⊤- Defined in
- Mathlib.RingTheory.Ideal.Cotangent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites23
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
- Setstatement and proof · cited by 53,352
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Top.topstatement and proof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Set.imagestatement and proof · cited by 5,609
- Idealstatement · cited by 4,748
- Submodule.spanstatement and proof · cited by 1,504
- Submodule.mapproof · cited by 614
- IsLocalRingstatement and proof · cited by 339
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