International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 8, Pages 457-465
doi:10.1155/S0161171201005713
Generalized periodic and generalized Boolean rings
1Department of Mathematics, Brock University, Ontario, Street Catharines L2S 3A1, Canada
2Department of Mathematics, University of California, Santa Barbara 93106, CA, USA
Received 21 August 2000
Copyright © 2001 Howard E. Bell 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
We prove that a generalized periodic, as well as a generalized Boolean, ring is either commutative or periodic. We also prove that a generalized Boolean ring with central idempotents must be nil or commutative. We further consider conditions which imply the commutativity of a generalized periodic, or a generalized Boolean, ring.