한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)
- 제10권3호
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- Pages.177-183
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- 2003
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- 1226-0657(pISSN)
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- 2287-6081(eISSN)
ANNIHILATOR CONDITIONS ON RINGS AND NEAR-RINGS
초록
In this paper, we initiate the study of some annihilator conditions on polynomials which were used by Kaplansky [Rings of operators. W. A. Benjamin, Inc., New York, 1968] to abstract the algebra of bounded linear operators on a Hilbert spaces with Baer condition. On the other hand, p.p.-rings were introduced by Hattori [A foundation of torsion theory for modules over general rings. Nagoya Math. J. 17 (1960) 147-158] to study the torsion theory. The purpose of this paper is to introduce the near-rings with Baer condition and near-rings with p.p. condition which are somewhat different from ring case, and to extend a results of Armendariz [A note on extensions of Baer and P.P.-rings. J. Austral. Math. Soc. 18 (1974), 470-473] and Jøndrup [p.p. rings and finitely generated flat ideals. Proc. Amer. Math. Soc. 28 (1971) 431-435].