International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 67692, 6 pages

Structure of rings with certain conditions on zero divisors

Hazar Abu-Khuzam1 and Adil Yaqub2

1Department of Mathematics, American University of Beirut, Beirut 1107 2020, Lebanon
2Department of Mathematics, University of California, Santa Barbara 93106-3080, CA, USA

Received 4 May 2004; Revised 17 September 2004; Accepted 24 July 2006

Copyright © 2006 Hazar Abu-Khuzam and Adil Yaqub. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 ab=ba. 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.