International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 15, Article ID 67692, 6 pages
doi:10.1155/IJMMS/2006/67692
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
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 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.