IJPAM: Volume 54, No. 4 (2009)

ON THE STRUCTURES OF QUOTIENT GROUPS

Omolo N. Ongati$^1$, Owino Maurice Oduor$^2$
$^{1,2}$Department of Mathematics and Applied Statistics
Maseno University
P.O. Box 333, Maseno, KENYA
$^1$e-mail: omolo_ongati@yahoo.com
$^2$e-mail: morricearaka@yahoo.com


Abstract.Let $J$ be the Jacobson radical of a commutative completely primary finite ring $R$ such that $J^{k}\neq(0)$ and $J^{k+1}=(0).$ Then $R/J\cong GF(p^{r})$, the finite field of $p^{r}$ elements, and the characteristic of $R$ is $p^{k}$ where $k\geq 2$ and $p$ is some prime integer. In this paper, we determine the structures of the quotient groups $1+J^{i}/1+J^{i+1}$ for every characteristic of $R$ and $1\leq i\leq k-1$.

Received: May 22, 2009

AMS Subject Classification: 13M05, 16U60

Key Words and Phrases: quotient groups, completely primary finite rings

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 4