# Answer to Question #16543 in Algebra for Tsit Lam

Question #16543

Let R be a ring possibly without an identity. Show that if R has a unique left identity e, then e is also a right identity

Expert's answer

Suppose

(

Therefore,

*e**∈**R*is a*unique*left identity for*R*. Then for any*a, c**∈**R*,(

*e*+*ae − a*)*c*=*c*+*ac − ac*=*c.*Therefore,

*e*+*ae − a*=*e*, which implies*ae*=*a*(for any*a**∈ R*).Need a fast expert's response?

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