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JP Journal of Algebra, Number Theory and Applications

JP Journal of Algebra, Number Theory and Applications
Volume 3, Issue 3, Pages 351 - 358 (December 2003)

A STUDY ON BAER LIKE NEAR-RINGS
Yong Uk Cho (Korea)

Abstract:
Hattori [Nagoya Math. J. 17 (1960), 147-158] introduced the left p.p.-rings and Kaplansky [Rings of operators, Math. Lecture Notes Series, Benjamin, New York, 1968] introduced the Baer rings. In 1974, Armendariz obtained the result ([Austral. Math. Soc. 18 (1974),470-473], Theorem B): In a reduced ring R, R is a Baer ring if and only if the polynomial ring R[x] is Baer.

The purpose of this paper is to investigate the relations between near-rings with Baer condition and Baer rings, also near-rings with P.P. condition and p.p.-rings. They are somewhat different from the ring case.

Keywords and phrases: reduced, Baer near-rings, p.p.-near-rings.

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