• Chen, Huanyin (Department of Mathematics Hangzhou Normal University)
  • Received : 2009.01.21
  • Published : 2010.05.31


Let R be a ring, and let $\Psi$(R) be the ideal generated by the set {x $\in$R | 1 + sxt $\in$ R is unit-regular for all s, t $\in$ R}. We show that $\Psi$(R) has "radical-like" property. It is proven that $\Psi$(R) has stable range one. Thus, diagonal reduction of matrices over such ideal is reduced.


unit-regularity;stable range one;diagonal reduction


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