Theorems · Theorem · commutative algebra
Ideal.isIdempotentElem_iff_eq_bot_or_top_of_isLocalRing
∀ {R : Type u_3} [inst : CommRing R] [IsNoetherianRing R] [IsLocalRing R] (I : Ideal R),
IsIdempotentElem I ↔ I = ⊥ ∨ I = ⊤Also see Ideal.isIdempotentElem_iff_eq_bot_or_top for integral domains.
- Defined in
- Mathlib.RingTheory.Filtration
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Top.topstatement and proof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- pow_zeroproof · cited by 1,094
- IsLocalRingstatement and proof · cited by 339
- IsNoetherianRingstatement and proof · cited by 268
- IsIdempotentElemstatement and proof · cited by 217
- eq_bot_iffproof · cited by 159
- le_iInfproof · cited by 102
- Ideal.one_eq_topproof · cited by 83
- Ideal.mul_topproof · cited by 42
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalRing.subsingleton_cotangentSpace_iffproof · cited by 1