Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON 2 × 2 STRONGLY CLEAN MATRICES

  • Chen, Huanyin (Department of Mathematics Hangzhou Normal University)
  • Received : 2011.05.26
  • Published : 2013.01.31
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Abstract

An element in a ring R is strongly clean provided that it is the sum of an idempotent and a unit that commutate. In this note, several necessary and sufficient conditions under which a $2{\times}2$ matrix over an integral domain is strongly clean are given. These show that strong cleanness over integral domains can be characterized by quadratic and Diophantine equations.

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References

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