DOI QR코드

DOI QR Code

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

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.

키워드

참고문헌

  1. S. A. Amitsur, Radicals of polynomial rings, Canad. J. Math. 8 (1956), 355-361. https://doi.org/10.4153/CJM-1956-040-9
  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.
  4. V. Camillo, C. Y. Hong, N. K. Kim, Y. Lee, and P. P. Nielsen, Nilpotent ideals in polynomial and power series rings, Proc. Amer. Math. Soc. 138 (2010), no. 5, 1607-1619. https://doi.org/10.1090/S0002-9939-10-10252-4
  5. C. Huh, H. K. Kim, and Y. Lee, p.p. rings and generalized p.p. rings, J. Pure Appl. Algebra 167 (2002), no. 1, 37-52. https://doi.org/10.1016/S0022-4049(01)00149-9
  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