Near-rings with left Baer like conditions
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Kaplansky introduced the Baer rings as rings in which everyleft (or right) annihilator of each subset is generated by an idempotent.On the other hand, Hattori introduced the left (resp. right) P.P. ringsas rings in which every principal left (resp. right) ideal is projective.The purpose of this paper is to introduce the near-rings with Baer likecondition and near-rings with P.P. like condition which are somewhatdierent from ring case, and to extend the results of Armendariz andJøndrup.
Abstract
Kaplansky introduced the Baer rings as rings in which everyleft (or right) annihilator of each subset is generated by an idempotent.On the other hand, Hattori introduced the left (resp. right) P.P. ringsas rings in which every principal left (resp. right) ideal is projective.The purpose of this paper is to introduce the near-rings with Baer likecondition and near-rings with P.P. like condition which are somewhatdierent from ring case, and to extend the results of Armendariz andJøndrup.
참고문헌 (9)
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- S. K. Berberian, "Baer *-Rings" (1972), Springer-Verlag
- A. Hattori, "A foundation of torsion theory for modules over general rings", Nagoya Mathematics Journal, 17, pp.147~158 (1960)
- S. Jøndrup, "P.P. rings and finitely generated flat ideals", Proceedings of the American Mathematical Society, 28, pp.431~435 (1971)
- I. Kaplansky, "Rings of Operators" (1968), W. A. Benjamin, Inc.
- J. D. P. Meldrum, "Near-Rings and Their Links with Groups" (1985), Pitman (Advanced Publishing Program)
- G. Pilz, "Near-Rings" (1983), North-Holland Publishing Co.
- D. Ramakotaiah, "Reduced near-rings, Near-rings and near-fields (Tubingen, 1985)", North-Holland Mathematics Studies, 137, pp.233~243 (1987)