| Title:
|
Restricted Boolean group rings (English) |
| Author:
|
Udar, Dinesh |
| Author:
|
Sharma, R.K. |
| Author:
|
Srivastava, J.B. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
155-159 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study restricted Boolean rings and group rings. A ring $R$ is $\textit{restricted Boolean}$ if every proper homomorphic image of $R$ is boolean. Our main aim is to characterize restricted Boolean group rings. A complete characterization of non-prime restricted Boolean group rings has been obtained. Also in case of prime group rings necessary conditions have been obtained for a group ring to be restricted Boolean. A counterexample is given to show that these conditions are not sufficient. (English) |
| Keyword:
|
group rings |
| Keyword:
|
restricted Boolean rings |
| Keyword:
|
Boolean rings |
| Keyword:
|
neat rings |
| Keyword:
|
prime group rings |
| MSC:
|
16S34 |
| MSC:
|
20C05 |
| MSC:
|
20C07 |
| idZBL:
|
Zbl 06819522 |
| idMR:
|
MR3708769 |
| DOI:
|
10.5817/AM2017-3-155 |
| . |
| Date available:
|
2017-09-13T09:32:15Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146881 |
| . |
| Reference:
|
[1] Brown, B., McCoy, N.H.: The maximal regular ideal of a ring.Proc. Amer. Math. Soc. 1 (2) (1950), 165–171. Zbl 0036.29702, MR 0034757, 10.1090/S0002-9939-1950-0034757-7 |
| Reference:
|
[2] Connell, I.G.: On the group ring.Canad. J. Math. 15 (1963), 650–685. Zbl 0121.03502, MR 0153705, 10.4153/CJM-1963-067-0 |
| Reference:
|
[3] Kaplansky, I.: Notes on ring theory.Mimeographed lecture notes. University of Chicago (1965). |
| Reference:
|
[4] Lam, T.Y.: A First Course in Noncommutative Rings.second ed., Springer Verlag New York, 2001. Zbl 0980.16001, MR 1838439 |
| Reference:
|
[5] McGovern, W.Wm.: Neat rings.J. Pure Appl. Algebra 205 (2006), 243–265. Zbl 1095.13025, MR 2203615, 10.1016/j.jpaa.2005.07.012 |
| Reference:
|
[6] Passman, D.S.: The Algebraic Structure of Group Rings.John Wiley and Sons, New York, 1977. Zbl 0368.16003, MR 0470211 |
| . |
