Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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DISTRIBUTIVE PROPERTIES OF ADDITION OVER MULTIPLICATION OF IDEMPOTENT MATRICES

  • Received : 2001.04.23
  • Accepted : 2011.06.01
  • Published : 2011.09.30
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Abstract

Let R be a ring with identity. If a, b, $c{\in}R$ such that a+b+c = 1, then the distributive laws from addition over multiplication hold in R, that is a+(bc) = (a+b)(a+c) when ab = ba, and (ab)+c = (a+c)(b+c) when ac = ca. An application to obtains, if A,B are idempotent matrices and AB = BA = 0 then there exists an idempotent matrix C such that A + BC = (A + B)(A + C), and also A + BC = (I - C)(I - B). Some other cases and applications are also presented.

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References

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