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

Howard E. Bell1 and Adil Yaqub2

 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

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.