International Journal of Mathematics and Mathematical Sciences 
Volume 22 (1999), Issue 1, Pages 67-74
doi:10.1155/S0161171299220674

Noncommutativity and noncentral zero divisors

Howard E. Bell1 and Abraham A. Klein2

 1Department of Mathematics, Brock University, ST. Catharines, Ontario, L2S 3A1, Canada
2Sackler Faculty of Exact Sciences, School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel
Received 11 September 1997

Abstract

Let R be a ring, Z its center, and D the set of zero divisors. For finite noncommutative rings, it is known that D\Z≠∅. We investigate the size of |D\Z| in this case and, also, in the case of infinite noncommutative rings with D\Z≠∅.