Theorems · Theorem · commutative algebra
Ideal.isIdempotentElem_iff_eq_bot_or_top
∀ {R : Type u_1} [inst : CommRing R] [IsDomain R] (I : Ideal R), I.FG → (IsIdempotentElem I ↔ I = ⊥ ∨ I = ⊤)- Defined in
- Mathlib.RingTheory.Ideal.IdempotentFG
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
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
- IsDomainstatement and proof · cited by 2,196
- Submodule.spanproof · cited by 1,504
- IsIdempotentElemstatement and proof · cited by 217
- Ideal.FGstatement and proof · cited by 99
- Ideal.mul_topproof · cited by 42
- Ideal.submodule_span_eqproof · cited by 25
- Ideal.span_singleton_oneproof · cited by 21
- Submodule.mul_botproof · cited by 9
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