International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 1, Pages 197-199

On topologies over rings

Syed M. Fakhruddin

Department of Mathematics, University of Petroleum and Minerals, Dhahran, Saudi Arabia

Received 4 February 1983; Revised 24 June 1983

Copyright © 1985 Syed M. Fakhruddin. 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.


In this note, we show that if a topology F¯ over a ring A satisfies a certain finiteness condition, then the Gabriel topology G¯ generated by F¯ can be explicitly constructed and it also satisfies the same finiteness condition.