Theorems · Theorem · commutative algebra
IsLocalRing.subsingleton_cotangentSpace_iff
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsLocalRing R] [IsNoetherianRing R],
Subsingleton (IsLocalRing.CotangentSpace R) ↔ IsField R- Defined in
- Mathlib.RingTheory.Ideal.Cotangent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Bot.botproof · cited by 4,720
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealproof · cited by 297
- IsNoetherianRingstatement and proof · cited by 268
- IsIdempotentElemproof · cited by 217
- IsFieldstatement · cited by 103
- Ideal.IsMaximal.ne_topproof · cited by 42
- IsLocalRing.CotangentSpacestatement · cited by 16
- IsLocalRing.isField_iff_maximalIdeal_eqproof · cited by 8
- Ideal.cotangent_subsingleton_iffproof · cited by 3
- Ideal.isIdempotentElem_iff_eq_bot_or_top_of_isLocalRingproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalRing.finrank_cotangentSpace_eq_zero_iffproof · cited by 1