International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 67692, 6 pages
Structure of rings with certain conditions on zero divisors
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 be a ring such that every zero divisor is expressible as a sum of a nilpotent element and a potent element of , where is nilpotent, is potent, and . We call such a ring a -ring. We give the structure of periodic -ring, weakly periodic -ring, Artinian -ring, semiperfect -ring, and other classes of -ring.