IJPAM: Volume 57, No. 1 (2009)

UNIT GROUPS OF $k+1$ INDEX
RADICAL ZERO COMMUTATIVE FINITE RINGS

Owino Maurice Oduor$^1$, Chiteng'a John Chikunji$^2$, Omolo N. Ongati$^3$
$^{1,3}$Department of Mathematics and Applied Statistics
Maseno University
Maseno, KENYA
$^1$e-mail: [email protected]
$^2$Department of Basic Sciences
Botswana College of Agriculture
Gaborone, BOTSWANA
e-mail: [email protected]


Abstract.In this paper, we determine the structures of the unit groups of commutative finite rings $R$ of characteristic $p^{k}$ where $p$ is any prime integer and $k$ is any positive integer such that if $J$ is the Jacobson radical of $R$, then $J^{k+1}=(0),$ $J^{k}\neq (0)$ and $R/J\cong GF(p^{r})$, the finite field of $p^{r}$ elements for any prime $p$ and any positive integer $r.$

Received: August 30, 2009

AMS Subject Classification: 13M05, 16U60

Key Words and Phrases: unit groups, commutative finite rings

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 1