Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SOME STRONGLY NIL CLEAN MATRICES OVER LOCAL RINGS

  • Chen, Huanyin (Department of Mathematics Hangzhou Normal University)
  • Received : 2009.12.08
  • Published : 2011.07.31
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Abstract

An element of a ring is called strongly nil clean provided that it can be written as the sum of an idempotent and a nilpotent element that commute. A ring is strongly nil clean in case each of its elements is strongly nil clean. We investigate, in this article, the strongly nil cleanness of 2${\times}$2 matrices over local rings. For commutative local rings, we characterize strongly nil cleanness in terms of solvability of quadratic equations. The strongly nil cleanness of a single triangular matrix is studied as well.

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References

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