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International Journal of Mathematics and Mathematical Sciences
Volume 13, Issue 3, Pages 535-544
http://dx.doi.org/10.1155/S0161171290000771

Some conditions for finiteness and commutativity of rings

Department of Mathematics, Brock University, Ontario, St. Catharines L2S 3A1, Canada

Received 21 March 1989; Revised 9 September 1989

Copyright © 1990 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 present several new sufficient conditions for a ring to be finite; we give two conditions which for periodic rings R imply that R must be either finite or commutative; and we study commutativity in rings with only finitely many non-central subrings.