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
Doostali Mojdeh
and S.Hassan Hashemi
Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran
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.