Editing Endomorphism ring (section)

== Description ==
Let {{nowrap|(''A'', +)}} be an abelian group and we consider the group homomorphisms from ''A'' into ''A''. Then addition of two such homomorphisms may be defined pointwise to produce another group homomorphism. Explicitly, given two such homomorphisms ''f'' and ''g'', the sum of ''f'' and ''g'' is the homomorphism {{nowrap|''f'' + ''g'' : ''x'' ↦ ''f''(''x'') + ''g''(''x'')}}. Under this operation End(''A'') is an abelian group. With the additional operation of composition of homomorphisms, End(''A'') is a ring with multiplicative identity. This composition is explicitly {{nowrap|''fg'' : ''x'' ↦ ''f''(''g''(''x''))}}. The multiplicative identity is the identity homomorphism on ''A''. The additive inverses are the pointwise inverses. 

If the set ''A'' does not form an ''abelian'' group, then the above construction is not necessarily well-defined, as then the sum of two homomorphisms need not be a homomorphism.{{sfn|ps=none|Dummit|Foote|p=347}} However, the closure of the set of endomorphisms under the above operations is a canonical example of a [[near-ring]] that is not a ring.