Abstract
Let A be the free algebra on one generator satisfying the left distributive law a ( b c ) = ( a b ) ( a c ) . Using a division algorithm for elements of an extension P of A , we prove some facts about left division in A , one consequence of which is a conjecture of J. Moody: If a , b , c , d ∈ A , a b = c d , a and b have no common left divisors, and c and d have no common left divisors, then a = c and b = d .
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