충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제32권4호
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  • Pages.401-408
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  • 2019
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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ON NILPOTENT-DUO RINGS

  • Piao, Zhelin (Department of Mathematics Yanbian University)
  • 투고 : 2019.05.27
  • 심사 : 2019.08.21
  • 발행 : 2019.11.15
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초록

A ring R is called right (resp., left) nilpotent-duo if N(R)a ⊆ aN(R) (resp., aN(R) ⊆ N(R)a) for every a ∈ R, where N(R) is the set of all nilpotents in R. In this article we provide other proofs of known results and other computations for known examples in relation with right nilpotent-duo property. Furthermore we show that the left nilpotent-duo property does not go up to a kind of matrix ring.

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참고문헌

  1. Y.W. Chung and Y. Lee, Structures concerning group of units, J. Korean Math. Soc., 54 (2017), 177-191. https://doi.org/10.4134/JKMS.j150666
  2. R.C. Courter, Finite dimensional right duo algebras are duo, Proc. Amer. Math. Soc., 84 (1982), 157-161. https://doi.org/10.1090/S0002-9939-1982-0637159-6
  3. E.H. Feller, Properties of primary noncommutative rings, Trans. Amer. Math. Soc., 89 (1958), 79-91. https://doi.org/10.1090/S0002-9947-1958-0098763-0
  4. C.Y. Hong, H.K. Kim, N.K. Kim, T.K. Kwak, and Y. Lee, One-sided duo property on nilpotents, (Submitted).