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Structure of rings with certain conditions on zero divisors

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  • Hazar Abu-Khuzam
  • Adil Yaqub

Abstract

Let R be a ring such that every zero divisor x is expressible as a sum of a nilpotent element and a potent element of R : x = a + b , where a is nilpotent, b is potent, and a b = b a . We call such a ring a D * -ring. We give the structure of periodic D * -ring, weakly periodic D * -ring, Artinian D * -ring, semiperfect D * -ring, and other classes of D * -ring.

Suggested Citation

  • Hazar Abu-Khuzam & Adil Yaqub, 2006. "Structure of rings with certain conditions on zero divisors," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-6, September.
    • Handle: RePEc:hin:jijmms:067692
    DOI: 10.1155/IJMMS/2006/67692
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