International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 2, Pages 83-89

Subgroups of finite index in an additive group of a ring

Doostali Mojdeh and S. Hassan Hashemi

Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran

Received 15 March 2000; Revised 10 June 2000

Copyright © 2001 Doostali Mojdeh and S. Hassan Hashemi. 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.


If K is an infinite field and GK is a subgroup of finite index in an additive group, then K=GG1 where G denotes the set of all invertible elements in G and G1 denotes all inverses of elements of G. Similar results hold for various fields, division rings and rings.