대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제32권3호
  • /
  • Pages.503-509
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  • 2017
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON WEAKLY LEFT QUASI-COMMUTATIVE RINGS

  • Kim, Dong Hwa (Department of Mathematics Education Pusan National University) ;
  • Piao, Zhelin (Department of Mathematics Yanbian University) ;
  • Yun, Sang Jo (Department of Mathematics Dong-A University)
  • 투고 : 2016.07.25
  • 심사 : 2016.10.05
  • 발행 : 2017.07.31
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초록

We in this note consider a generalized ring theoretic property of quasi-commutative rings in relation with powers. We will use the terminology of weakly left quasi-commutative for the class of rings satisfying such property. The properties and examples are basically investigated in the procedure of studying idempotents and nilpotent elements.

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참고문헌

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  2. H. E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc. 2 (1970), 363-368. https://doi.org/10.1017/S0004972700042052
  3. G. F. Birkenmeier, H. E. Heatherly, and E. K. Lee, Completely prime ideals and associated radicals, Proc. Biennial Ohio State-Denison Conference 1992, edited by S. K. Jain and S. T. Rizvi, World Scientific, 102-129, Singapore-New Jersey-London-Hong Kong, 1993.
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  6. C. Huh, N. K. Kim, and Y. Lee, Examples of strongly ${\pi}$-regular rings, J. Pure Appl. Algebra 189 (2004), no. 1-3, 195-210. https://doi.org/10.1016/j.jpaa.2003.10.032
  7. C. Huh, Y. Lee, and A. Smoktunowicz, Armendariz rings and semicommutative ring, Comm. Algebra 30 (2002), no. 2, 751-761. https://doi.org/10.1081/AGB-120013179
  8. D. W. Jung, B.-O. Kim, H. K. Kim, Y. Lee, S. B. Nam, S. J. Ryu, H. J. Sung, and S. J. Yun On quasi-commutative rings, J. Korean Math. Soc. 53 (2016), no. 2, 475-488. https://doi.org/10.4134/JKMS.2016.53.2.475