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International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 8, Pages 457-465
http://dx.doi.org/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, CA 93106, USA

Received 21 August 2000

Copyright © 2001 Hindawi Publishing Corporation. 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.