Theorems · Definition · ring theory
Module.End
(R : Type u) → (M : Type v) → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [Module R M] → Type v
Linear endomorphisms of a module, with associated ring structure
Module.End.semiring and algebra structure Module.End.algebra.
- Defined in
- Mathlib.Algebra.Module.LinearMap.End
- Cited by
- 774 results in Mathlib
- Foundations
- Depth 13 from the axioms, rests on 111 definitions · uses no axioms
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idproof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapproof · cited by 10,215
Cited by891
Results whose statement or proof uses this declaration.
- LieModule.toEndstatement · cited by 144
- Module.End.invtSubmodulestatement and proof · cited by 93
- IsBaseChangeproof · cited by 87
- Module.End.genEigenspacestatement and proof · cited by 70
- Module.End.HasEigenvaluestatement and proof · cited by 56
- Module.End.eigenspacestatement and proof · cited by 56
- LieAlgebra.adstatement · cited by 49
- Module.End.maxGenEigenspacestatement and proof · cited by 41
- LieModule.traceFormproof · cited by 41
- Algebra.lmulstatement and proof · cited by 41
- IsLocalizedModule.map_unitsstatement · cited by 40
- LieModule.toEnd_apply_applystatement · cited by 39
Showing the 200 most cited of 891.