Regular duo elements of abstract affine near-rings (Q2639942)

The author extends results of \textit{O. Steinfeld} [Stud. Sci. Math. Hung. 8, 161-164 (1973; Zbl 0286.20085)] to abstract affine near-rings, following his earlier work in this area [Proc. Jap. Acad., Ser. A 65, 307-310 (1989; Zbl 0705.16027), and ibid. 66, 115-118 (1990; Zbl 0713.16027)]. He is able to characterize regular duo elements in such near-rings, and when such near-rings are regular duo rings. An element is duo if the principal left ideal it generates is equal to the principal right ideal it generates.