International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 1, Pages 197-199
doi:10.1155/S0161171285000217
On topologies over rings
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.
Abstract
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.