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http://dx.doi.org/10.4134/BKMS.2008.45.2.263

NEAR-RINGS WITH LEFT BAER LIKE CONDITIONS  

Cho, Yong-Uk (Department of Mathematics Education College of Education Silla University)
Publication Information
Bulletin of the Korean Mathematical Society / v.45, no.2, 2008 , pp. 263-267 More about this Journal
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 Arendariz and Jondrup.
Keywords
Baer rings; left (resp. right) Baer near-rings; left (resp. right) P.P. rings and left (resp. right) P.P. near-rings;
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  • Reference
1 A. Hattori, A foundation of torsion theory for modules over general rings, Nagoya Math. J. 17 (1960), 147-158   DOI
2 G. Pilz, Near-Rings, North-Holland Publishing Co., Amsterdam, 1983
3 E. P. Armendariz, A note on extensions of Baer and P.P.-rings, J. Austral. Math. Soc. 18 (1974), 470-473   DOI
4 I. Kaplansky, Rings of Operators, W. A. Benjamin, Inc., New York-Amsterdam 1968
5 J. C. Beidleman, A note on regular near-rings, J. Indian Math. Soc. (N.S.) 33 (1969), 207-209
6 J. D. P. Meldrum, Near-Rings and Their Links with Groups, Pitman (Advanced Publishing Program), Boston, MA, 1985
7 D. Ramakotaiah and V. Sambasiva Rao, Reduced near-rings, Near-rings and near-fields (Tubingen, 1985), 233-243, North-Holland Math. Stud., 137, North-Holland, Amsterdam, 1987
8 S. K. Berberian, Baer *-Rings, Springer-Verlag, New York-Berlin, 1972
9 S. Jondrup, P.P. rings and finitely generated flat ideals, Proc. Amer. Math. Soc. 28 (1971), 431-435