A STUDY ON ANNIHILATOR CONDITIONS OF POLYNOMIALS

Abstract

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 Armendarz [1] to polynomial near-rings with Baer condition in somewhat different way of Birkenmeier and Huang [2].

Keywords

• endomorphisms;
• AE-fings;
• AGE-fings;
• AGOE-rings;
• LSD-generated;
• RSD-generated;
• SD-generated

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References

1. Australian Math. Soc. v.18 A note on extensions of Baer and p.p.rings E.P.Armendariz
2. Comm. in Algebra Annihilator conditions on polynomials G.F.Birkenmeier;F.K.Huang
3. Nagoya Math. J. v.17 A foundation of the torsion theory over general rings A.Hattori
4. Math. Lecture Notes Series Rings of Operators I.Kaplansky
5. Near-Rings and Their Links with Groups J.D.P.meldrum
6. Near-Rings G.Pilz
7. Near-rings and Near-fields Reduced near-ring D.Ramakotaiah;V.Sambasivarao;G.Betsch(ed.)