International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 2, Pages 83-89
doi:10.1155/S0161171201010274
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.
Abstract
If K is an infinite field and G⫅K is a subgroup of
finite index in an additive group, then K∗=G∗G∗−1 where G∗ denotes the set of all invertible elements
in G and G∗−1 denotes all inverses of elements of G∗. Similar results hold for various fields, division rings and rings.