Theorems · Theorem · linear algebra
LinearMap.isIdempotentElem_map_one_iff
∀ {R : Type u_1} [inst : Semiring R] {f : Module.End R R}, IsIdempotentElem (f 1) ↔ IsIdempotentElem f- Defined in
- Mathlib.LinearAlgebra.Span.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- mul_oneproof · cited by 3,885
- Module.Endstatement and proof · cited by 774
- map_smulproof · cited by 566
- smul_eq_mulproof · cited by 357
- IsIdempotentElemstatement and proof · cited by 217
- LinearMap.ext_iffproof · cited by 32
Cited by1
Results whose statement or proof uses this declaration.
- IsSemisimpleRing.ideal_eq_span_idempotentproof · cited by 0