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.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201010274 |
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| _version_ | 1850173412683546624 |
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| author | Doostali Mojdeh S. Hassan Hashemi |
| author_facet | Doostali Mojdeh S. Hassan Hashemi |
| author_sort | Doostali Mojdeh |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d2ce350f4bbc41b19d2f417ac00a37d0 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d2ce350f4bbc41b19d2f417ac00a37d02025-08-20T02:19:51ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-01272838910.1155/S0161171201010274Subgroups of finite index in an additive group of a ringDoostali Mojdeh0S. Hassan Hashemi1Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, IranDepartment of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, IranIf 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.http://dx.doi.org/10.1155/S0161171201010274 |
| spellingShingle | Doostali Mojdeh S. Hassan Hashemi Subgroups of finite index in an additive group of a ring International Journal of Mathematics and Mathematical Sciences |
| title | Subgroups of finite index in an additive group of a ring |
| title_full | Subgroups of finite index in an additive group of a ring |
| title_fullStr | Subgroups of finite index in an additive group of a ring |
| title_full_unstemmed | Subgroups of finite index in an additive group of a ring |
| title_short | Subgroups of finite index in an additive group of a ring |
| title_sort | subgroups of finite index in an additive group of a ring |
| url | http://dx.doi.org/10.1155/S0161171201010274 |
| work_keys_str_mv | AT doostalimojdeh subgroupsoffiniteindexinanadditivegroupofaring AT shassanhashemi subgroupsoffiniteindexinanadditivegroupofaring |