Abstract:
In this article we examine $m\Omega$-near-rings, i.e. $(m+1)$-ary associative ringoids over $\Omega$-groups with one supplementary condition. The concept of a module over an $m\Omega$-near-ring is introduced and, with its aid, the concept of a primitive $m\Omega$-near-ring is introduced, generalizing the idea of a primitive ring. Density theorems are proved for such $m\Omega$-near-rings. With the aid of these theorems, primitive $m\Omega$-near-rings with minimum condition for right ideals are described, and a series of theorems are proved concerning the structure of $m\Omega$-near-rings, which are analogous to simple rings with minimal one-sided ideals.
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