On right alternative rings without proper right ideals

Literature Survey on Non-Associative Rings and Developments

“…Also applied the results to amplify comments by Humm and Kleinfeld work on free alternative rings and contained examples of alternative rings. Slater [228] in 1968 discussed the ideals in semiprime alternative rings and also the results of the paper, so far concerned that a given right ideal A, did not require semiprimeness of R. In 1969, Kleinfeld [139] worked on right alternative rings without proper right ideals he showed that a right alternative ring R without proper right ideals, of characteristic not two, containing idempotents e and 1,e = 1, such that ex = e(ex) for all x ∈ R must be alternative and hence a cayley vector matrix algebra of dimension 8 over its center. Moreover, Slater [229] in 1969, proved the natural extension to arbitrary rings of the classical Wedderburn-Artin theorem for associative ones.…”