Distributive elements and endomorphisms of a near-ring
Let N be a right zero-symmetric near-ring with identity. In this note the following are proved to be equivalent: i) the distributive part \(N_ d\) of N is a ring; ii) \((N,+)\) is abelian; iii) the left near-ring Ass(N) associated to N is a ring. Besides N is shown to be a faithful, monogenic and unitary right Ass(N)-group whose centralizer is isomorphic to the monoid \((N_ d,\cdot)\).
scientific article; zbMATH DE number 4029782