Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON EXCHANGE qb-IDEALS

  • CHEN, HUANYIN (Department of Mathematics, Zhejiang Normal University) ;
  • CHEN, MIAOSEN (Department of Mathematics, Zhejiang Normal University)
  • Published : 2005.02.01
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Abstract

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.

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References

  1. P. Ara, Extensions of Exchange Rings, J. Algebra 197 (1997), 409-423 https://doi.org/10.1006/jabr.1997.7116
  2. P. Ara, K. R. Goodearl, K. C. O'Meara, and R. Raphael, Kl of Separative Exchange Rings and C' -Algebras with Real Rank Zero, Pacific J. Math. 195 (2000), 261-275 https://doi.org/10.2140/pjm.2000.195.261
  3. P. Ara, G. K. Pedersen, and F. Perera, An Infinite Analogue of Rings with Stable Range One, J. Algebra 230 (2000), 608-655 https://doi.org/10.1006/jabr.2000.8330
  4. P. Ara, Extensions and Pullbacks in QB-Rings, Preprint , 2000
  5. H. Chen, On Exchange QB-Ideals, 2003
  6. H. Chen, On Exchange QB-Rings, Comm. Algebra 31 (2003), 831-841 https://doi.org/10.1081/AGB-120017345
  7. H. Chen, Related Comparability over Exchange Rings, Comm. Algebra 27 (1999), 4209-4216 https://doi.org/10.1080/00927879908826691
  8. R. Guralnick and C. Lanski, Pseudosimilarity and Cancellation of Modules, Linear Algebra Appl. 47 (1982), 111-115 https://doi.org/10.1016/0024-3795(82)90228-2
  9. R. E. Hartwig and J. Luh, A Note on the Group Structure of Unit Regular Ring Elements, Pacific J. Math. 71 (1977), 449-461 https://doi.org/10.2140/pjm.1977.71.449
  10. P. Menal and J. Moncasi, Lifting Units in Self-injective Rings and An Index Theory for Rickert C'-Algebras, Pacific J. Math. 126 (1987), 295-329 https://doi.org/10.2140/pjm.1987.126.295
  11. F. Perera, Lifting Units Modulo Exchange Ideals and C'-Algebras with Real Rank Zero, J. Reine. Math. 522 (2000), 51-62
  12. H. P. Yu, Stable Range One for Rings with Many Idempotents, Trans. Amer. Math. Soc. 347 (1995), 3141-3147 https://doi.org/10.2307/2154778