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UNIT-REGULARITY AND STABLE RANGE ONE

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

Abstract

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.

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  2. Jacobson’s Lemma via Gröbner-Shirshov Bases vol.24, pp.02, 2017, https://doi.org/10.1142/S1005386717000189
  3. Inner inverses and inner annihilators in rings vol.397, 2014, https://doi.org/10.1016/j.jalgebra.2013.08.023