• Title, Summary, Keyword: qb-ideal

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ON EXCHANGE qb-IDEALS

  • CHEN, HUANYIN;CHEN, MIAOSEN
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.1
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    • pp.45-51
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    • 2005
  • In this paper, we establish necessary and sufficient conditions for an exchange ideal to be a qb-ideal. It is shown that an exchange ideal I of a ring R is a qb-ideal if and only if when-ever $a{\simeq}b$ via I, there exists u ${\in} I_q^{-1}$ such that a = $ubu_q^{-1}$ and b = $u_q^{-1}$. This gives a generalization of the corresponding result of exchange QB-rings.

ON QB-IDEALS OF EXCHANGE RINGS

  • Chen, Huanyin
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.5
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    • pp.873-884
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    • 2009
  • We characterize QB-ideals of exchange rings by means of quasi-invertible elements and annihilators. Further, we prove that every $2\times2$ matrix over such ideals of a regular ring admits a diagonal reduction by quasi-inverse matrices. Prime exchange QB-rings are studied as well.