• Chen, Huanyin (Department of Mathematics Hangzhou Normal University) ;
  • Sheibani, Marjan (Faculty of Mathematics Statistics and Computer Science Semnan University)
  • Received : 2015.01.21
  • Published : 2016.01.31


We prove, in this note, that a Zabavsky ring R is an elementary divisor ring if and only if R is a $B{\acute{e}}zout$ ring. Many known results are thereby generalized to much wider class of rings, e.g. [4, Theorem 14], [7, Theorem 4], [9, Theorem 1.2.14], [11, Theorem 4] and [12, Theorem 7].


elementary divisor ring;$B{\acute{e}}zout$ ring;Zabavsky ring;elementary matrix reduction


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