대한수학회지 (Journal of the Korean Mathematical Society)

  • 제44권4호
  • /
  • Pages.903-913
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  • 2007
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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WEAKLY STABLE CONDITIONS FOR EXCHANGE RINGS

  • Chen, Huanyin (DEPARTMENT OF MATHEMATICS HUNAN NORMAL UNIVERSITY)
  • 발행 : 2007.07.30
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초록

A ring R has weakly stable range one provided that aR+bR=R implies that there exists a $y{\in}R$ such that $a+by{\in}R$ is right or left invertible. We prove, in this paper, that every regular element in an exchange ring having weakly stable range one is the sum of an idempotent and a weak unit. This generalize the corresponding result of one-sided unit-regular ring. Extensions of power comparability and power cancellation are also studied.

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참고문헌

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