Answer to Question #16534 in Abstract Algebra for Hym@n B@ss
(1) Show that if a has a left inverse, then a is not a left 0-divisor.
(2) Show that the converse holds if a ∈ aRa.
(2) Write a = ara, and assume a is not a left 0-divisor. Then a(1 − ra) = 0 yields ra = 1, so a has left inverse r.
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