# ELEMENTARY MATRIX REDUCTION OVER ZABAVSKY RINGS

• Chen, Huanyin (Department of Mathematics Hangzhou Normal University) ;
• Sheibani, Marjan (Faculty of Mathematics Statistics and Computer Science Semnan University)
• Published : 2016.01.31
• 81 19

#### Abstract

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].

#### Keywords

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

#### References

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