Abstract
A well-known result by Y. Utumi states: Every right or left self-injective ring is von Neumann regular modulo its Jacobson radical. In this note, we give an example of a commutative ℵ0-self-injective ring which is not von Neumann regular modulo its Jacobson radical.
Mathematics Subject Classification:
ACKNOWLEDGMENT
The initial idea to construct a ring with the mentioned property, was inspired by Professor K. R. Goodearl, and the author would like to thank him. Also, I thank the referee for his/her careful reading and useful suggestions which improved this work effectively. Furthermore, the author thanks the Amini brothers for helpful discussions on the example.
Notes
Communicated by R. Wisbauer.
#Dedicated to Professor O. A. S. Karamzadeh.