Abstract
Let R be a prime ring and U(R) the group of units of R. We prove that if U(R) generates R and satisfies a group identity, then R is either a domain or a full matrix ring over a finite field.
| Original language | English |
|---|---|
| Pages (from-to) | 3305-3309 |
| Number of pages | 5 |
| Journal | Communications in Algebra |
| Volume | 31 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - 2003 Jul 1 |
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Keywords
- Generalized polynomial identities
- Group identities
- Prime rings
- Units
ASJC Scopus subject areas
- Algebra and Number Theory
Cite this
Group identities and prime rings generated by units. / Lee, Tsiu Kwen; Liu, Chia-Hsin.
In: Communications in Algebra, Vol. 31, No. 7, 01.07.2003, p. 3305-3309.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Group identities and prime rings generated by units
AU - Lee, Tsiu Kwen
AU - Liu, Chia-Hsin
PY - 2003/7/1
Y1 - 2003/7/1
N2 - Let R be a prime ring and U(R) the group of units of R. We prove that if U(R) generates R and satisfies a group identity, then R is either a domain or a full matrix ring over a finite field.
AB - Let R be a prime ring and U(R) the group of units of R. We prove that if U(R) generates R and satisfies a group identity, then R is either a domain or a full matrix ring over a finite field.
KW - Generalized polynomial identities
KW - Group identities
KW - Prime rings
KW - Units
UR - http://www.scopus.com/inward/record.url?scp=0042473892&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0042473892&partnerID=8YFLogxK
U2 - 10.1081/AGB-120022227
DO - 10.1081/AGB-120022227
M3 - Article
AN - SCOPUS:0042473892
VL - 31
SP - 3305
EP - 3309
JO - Communications in Algebra
JF - Communications in Algebra
SN - 0092-7872
IS - 7
ER -