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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 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).

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