Theorems · Theorem · ring theory
IsSemisimpleRing.ideal_eq_span_idempotent
∀ {R : Type u_2} [inst : Ring R] [IsSemisimpleRing R] (I : Ideal R), ∃ e, IsIdempotentElem e ∧ I = Ideal.span {e}- Defined in
- Mathlib.RingTheory.SimpleModule.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingIsSemisimpleRing
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Cites23
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- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Ringstatement and proof · cited by 7,463
- Submoduleproof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- Equiv.symmproof · cited by 3,681
- Submodule.spanproof · cited by 1,504
- Ideal.spanstatement and proof · cited by 948
- LinearMap.rangeproof · cited by 893
- Module.Endproof · cited by 774
- Submodule.mapproof · cited by 614
- IsComplproof · cited by 351
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