Subgroups of finite index in an additive group of a ring
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.
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201010274 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |