International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 2, Pages 239-242
doi:10.1155/S0161171288000286

Some conditions for finiteness of a ring

Abstract

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.