International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 2, Pages 239-242
Some conditions for finiteness of a ring
Department of Mathematics, Brock University, St. Catharines, Ontario L2S 3A1, Canada
Received 11 May 1987; Revised 24 June 1987
Copyright © 1988 Howard E. Bell. 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.
Extending a result of Putcha and Yaqub, we prove that a non-nil ring must be finite if it has both ascending chain condition and descending chain condition on non-nil subrings. We also prove that a periodic ring with only finitely many non-central zero divisors must be either finite or commutative.