International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 4, Pages 667-670
doi:10.1155/S0161171294000943
On rings with prime centers
1Department of Mathematics, American University of Beirut, Beirut, Lebanon
2Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California, USA
Received 4 December 1992; Revised 26 June 1993
Copyright © 1994 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.
Abstract
Let R be a ring, and let C denote the center of R. R is said to have a prime center if whenever ab belongs to C then a belongs to C or b belongs to C. The structure of certain classes of these rings is studied, along with the relation of the notion of prime centers to commutativity. An example of a non-commutative ring with a prime center is given.