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