Wedderburn-Artin theorem analogue for near-rings. (Q1887407)

The author considers only zero symmetric right near-rings with identity. He uses right ideals to obtain an analogue of the Wedderburn-Artin Theorem for rings. So a right completely reducible near-ring \(R\) is one which is a direct sum of strictly minimal right ideals (that is right ideals generated as right \(R\)-groups by any one non-zero element). Then he shows that a right completely reducible near-ring \(R\) with isomorphic strictly minimal right ideals is a simple near-ring containing a matrix near-ring over a near-field, and, if finite, is isomorphic to a matrix near-ring over a near-field if \(eRe\) is not a division ring for a strictly minimal right ideal \(eR\), \(e\) a distributive idempotent in \(R\). Also a near-ring is right completely reducible if and only if it is isomorphic to a finite direct product of right completely reducible simple near-rings. A simple near-ring is constructed which is the direct sum of two non-right-\(R\)-isomorphic minimal right ideals. Much use is made of the author's earlier paper [Quaest. Math. 17, No. 3, 321-332 (1994; Zbl 0818.16034)].