A ring primitive on the right but not on the left

Jacobson [1, p. 4] writes, is not known whether [right] primitivity implies left primitivity. It seems unlikely that it does, but no examples of [right] primitive rings which are not left primitive are known. Such an example is here constructed. Let D be a division ring, and a: D -D an endomorphism. Let A be the ring of formal polynomials Eizo diYi (dIED, nonzero for only finitely many i) with multiplication determined by the rule Yd =a(d) Y. Such rings are without zero divisors, and every left ideal of one is principal. The proofs are exactly as for the ordinary commutative rings of polynomials, cf. [2, p. 483]. Now let D = Q(X), where Q denotes the field of rationals, and let a be the map r(X)->r(X2). In this case, we have the following result.