Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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A PROOF ON POWER-ARMENDARIZ RINGS

  • Kim, Dong Hwa (Department of Mathematics Education Pusan National University) ;
  • Ryu, Sung Ju (Department of Mathematics Pusan National University) ;
  • Seo, Yeonsook (Department of Mathematics Pusan National University)
  • Received : 2012.10.17
  • Accepted : 2013.02.10
  • Published : 2013.03.30
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Abstract

Power-Armendariz is a unifying concept of Armendariz and commutative. Let R be a ring and I be a proper ideal of R such that R/I is a power-Armendariz ring. Han et al. proved that if I is a reduced ring without identity then R is power-Armendariz. We find another direct proof of this result to see the concrete forms of various kinds of subsets appearing in the process.

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Acknowledgement

Supported by : Pusan National University

References

  1. E.P. Armendariz, A note on extensions of Baer and P.P.-rings, J. Austral. Math. Soc. 18 (1974), 470-473. https://doi.org/10.1017/S1446788700029190
  2. J. Han, T.K. Kwak, M.J. Lee, Y. Lee, Y. Seo, On powers of coefficients of zero-dividing polynomials, (submitted).
  3. Y.C. Jeon, H.K. Kim, Y. Lee, J.S. Yoon, On weak Armendariz rings, Bull. Korean Math. Soc. 46 (2009), 135-146. https://doi.org/10.4134/BKMS.2009.46.1.135
  4. M.B. Rege, S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), 14-17. https://doi.org/10.3792/pjaa.73.14

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