• 제목/요약/키워드: LSD-generated ring

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A STUDY ON ADDITIVE ENDOMORPHISMS OF RINGS

  • Cho, Yong-Uk
    • 대한수학회보
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    • 제38권1호
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    • pp.149-156
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    • 2001
  • In this paper, we initiate the investigation of ring in which all the additive endomorphisms are generated by ring endomorphisms (AGE-rings). This study was motivated by the work on the Sullivan’s Research Problem [11]: Characterize those rings in which every additive endomorphism is a ring endomorphism (AE-rings). The purpose of this paper is to obtain a certain characterization of AGE-rings, and investigate some relations between AGE and LSD-generated rings.

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A STUDY ON ANNIHILATOR CONDITIONS OF POLYNOMIALS

  • Cho, Yong-Uk
    • 대한수학회보
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    • 제38권1호
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    • pp.137-142
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    • 2001
  • 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].

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