Theorems · Definition · group theory
IsIdempotentElem
{M : Type u_1} → [Mul M] → M → PropAn element a is said to be idempotent if a * a = a.
- Defined in
- Mathlib.Algebra.Group.Idempotent
- Cited by
- 217 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 8 definitions · uses no axioms
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by237
Results whose statement or proof uses this declaration.
- IsIdempotentElem.eqstatement and proof · cited by 42
- IsIdempotentElem.one_substatement and proof · cited by 20
- IsStarProjection.isIdempotentElemstatement · cited by 17
- ContinuousLinearMap.IsIdempotentElem.toLinearMapstatement · cited by 13
- PrimeSpectrum.isIdempotentElemEquivClopensstatement · cited by 10
- LinearMap.IsIdempotentElem.isProj_rangestatement · cited by 8
- IsIdempotentElem.pow_succ_eqstatement and proof · cited by 7
- OrthogonalIdempotents.idemstatement · cited by 7
- IsIdempotentElem.onestatement · cited by 7
- isStarProjection_iffstatement and proof · cited by 6
- LinearMap.IsSymmetricProjection.isIdempotentElemstatement · cited by 6
- AlgEquiv.prodQuotientOfIsIdempotentElemstatement and proof · cited by 5
Showing the 200 most cited of 237.