Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (6): 1587-1591.

• Articles • Previous Articles     Next Articles

Strongly J-clean Matrices over Group Rings

 CHEN Huan-Yin   

  1. Department of Mathematics, Hangzhou Normal University, Hangzhou 310036
  • Received:2013-07-14 Revised:2014-04-16 Online:2014-12-25 Published:2014-12-25
  • Supported by:

    浙江省自然科学基金(LY13A010019)资助

Abstract:

Let R be a ring, and let J(R) be the Jacobson radical of R. An element of a ring R is called strongly J-clean provided
that it can be written as the sum of an idempotent and an element in J(R) that commute. For a commutative local ring R with 2∈J(R), we get a necessary and sufficient condition under which a 2×2 matrix over RG is strongly J-clean where
G={ 1, g} is a group. An application to strong cleanness is also obtained

Key words: Strongly J-clean element, 2×2 Matrix, Commutative local ring

CLC Number: 

  • 16E50
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