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A GENERALIZATION OF ARMENDARIZ AND NI PROPERTIES

  • Li, Dan (Department of Mathematics Pusan National University) ;
  • Piao, Zhelin (Department of Mathematics Yanbian University) ;
  • Yun, Sang Jo (Department of Mathematics Dong-A University)
  • Received : 2017.07.11
  • Accepted : 2017.09.21
  • Published : 2018.07.31

Abstract

Antoine showed that the properties of Armendariz and NI are independent of each other. The study of Armendariz and NI rings has been doing important roles in the research of zero-divisors in noncommutative ring theory. In this article we concern a new class of rings which generalizes both Armendariz and NI rings. The structure of such sort of ring is investigated in relation with near concepts and ordinary ring extensions. Necessary examples are examined in the procedure.

Keywords

IPN ring;NI ring;Armendariz ring;polynomial ring;matrix ring;Abelian ring

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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