Bulletin of the
Korean Mathematical Society BKMS

In this paper, we initiate the study of some annihilator conditions on polynomials which were used by Kaplansky [4] to abstract algebras of bounded linear operators on a Hilbert spaces with Baer condition. On the other hand, p.p.\, rings were introduced by A. Hattori [3] to study the torsion theory. The purpose of this paper is to introduce near-rings with Baer condition and near-rings with p.p. condition which are somewhat different from the ring case, and to extend a results of Armendariz [1] to polynomial near-rings with Baer condition in somewhat different way of Birkenmeier and Huang [2].

Keywords: Baer rings, p.p.\, rings, Baer near-rings, p.p.\, near-rings

MSC numbers: 16Y30