On separable extensions of group rings and quaternion rings
The purposes of the present paper are (1) to give a necessary and sufficient condition for the uniqueness of the separable idempotent for a separable group ring extension RG(R may be a non-commutative ring), and (2) to give a full description of the set of separable idempotents for a quaternion ring...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1978-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171278000435 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850176801304739840 |
|---|---|
| author | George Szeto |
| author_facet | George Szeto |
| author_sort | George Szeto |
| collection | DOAJ |
| description | The purposes of the present paper are (1) to give a necessary and sufficient condition for the uniqueness of the separable idempotent for a separable group ring extension RG(R may be a non-commutative ring), and (2) to give a full description of the set of separable idempotents for a quaternion ring extension RQ over a ring R, where Q are the usual quaternions i,j,k and multiplication and addition are defined as quaternion algebras over a field. We shall show that RG has a unique separable idempotent if and only if G is abelian, that there are more than one separable idempotents for a separable quaternion ring RQ, and that RQ is separable if and only if 2 is invertible in R. |
| format | Article |
| id | doaj-art-bd9bea076de94e8cab487afe4bec9c64 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1978-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-bd9bea076de94e8cab487afe4bec9c642025-08-20T02:19:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251978-01-011443343810.1155/S0161171278000435On separable extensions of group rings and quaternion ringsGeorge Szeto0Mathematics Department, Bradley University, Peoria 61625, Illinois, USAThe purposes of the present paper are (1) to give a necessary and sufficient condition for the uniqueness of the separable idempotent for a separable group ring extension RG(R may be a non-commutative ring), and (2) to give a full description of the set of separable idempotents for a quaternion ring extension RQ over a ring R, where Q are the usual quaternions i,j,k and multiplication and addition are defined as quaternion algebras over a field. We shall show that RG has a unique separable idempotent if and only if G is abelian, that there are more than one separable idempotents for a separable quaternion ring RQ, and that RQ is separable if and only if 2 is invertible in R.http://dx.doi.org/10.1155/S0161171278000435group ringsidempotents in ringsseparable algebras. |
| spellingShingle | George Szeto On separable extensions of group rings and quaternion rings International Journal of Mathematics and Mathematical Sciences group rings idempotents in rings separable algebras. |
| title | On separable extensions of group rings and quaternion rings |
| title_full | On separable extensions of group rings and quaternion rings |
| title_fullStr | On separable extensions of group rings and quaternion rings |
| title_full_unstemmed | On separable extensions of group rings and quaternion rings |
| title_short | On separable extensions of group rings and quaternion rings |
| title_sort | on separable extensions of group rings and quaternion rings |
| topic | group rings idempotents in rings separable algebras. |
| url | http://dx.doi.org/10.1155/S0161171278000435 |
| work_keys_str_mv | AT georgeszeto onseparableextensionsofgroupringsandquaternionrings |