Bull. Korean Math. Soc. 2008 Vol. 45, No. 2, 263-267 Printed June 1, 2008
Yong Uk Cho Silla University
Abstract : Kaplansky introduced the Baer rings as rings in which every left (or right) annihilator of each subset is generated by an idempotent. On the other hand, Hattori introduced the left (resp. right) P.P. rings as rings in which every principal left (resp. right) ideal is projective. The purpose of this paper is to introduce the near-rings with Baer like condition and near-rings with P.P. like condition which are somewhat different from ring case, and to extend the results of Armendariz and J\o ndrup.
Keywords : Baer rings, left (resp. right) Baer near-rings, left (resp. right) P.P. rings and left (resp. right) P.P. near-rings