Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

ON NILPOTENT-DUO RINGS

  • Piao, Zhelin (Department of Mathematics Yanbian University)
  • Received : 2019.05.27
  • Accepted : 2019.08.21
  • Published : 2019.11.15
Download PDF
⟨ Previous Next ⟩

Abstract

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.

Keywords

References

  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).