On Baer and p.p.-near-rings. (Q2710503)

The author defines Baer near-rings as right near-rings in which every annihilator is the annihilator of an idempotent. Similarly a near-ring is a p.p.-near-ring if every annihilator of a single element is the annihilator of an idempotent. These definitions generalize the corresponding definitions for rings. Two of the main results proved in this paper show that the zero-symmetric near-ring of polynomials \(R_0[x]\) over a commutative ring with identity is a p.p.-near-ring if and only if \(R\) is a p.p.-ring, and that the same is true in the case of Baer near-ring and rings. Further results on these themes are proved.