Geodesic
Automorphisms of completely primary finite rings of characteristic $p$
Chiteng'a John Chikunji1
1 Department of Basic Sciences Botswana College of Agriculture P/BAG 0027, Gaborone, Botswana
Colloquium Mathematicum, Tome 111 (2008) no. 1, pp. 91-113

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

A completely primary ring is a ring $R$ with identity $1\neq 0$ whose subset of zero-divisors forms the unique maximal ideal ${\cal J}$. We determine the structure of the group of automorphisms ${\rm Aut}(R)$ of a completely primary finite ring $R$ of characteristic $p,$ such that if ${\cal J}$ is the Jacobson radical of $R,$ then ${\cal J}^{3}=(0),$ ${\cal J}^{2}\neq (0),$ the annihilator of ${\cal J}$ coincides with ${\cal J}^{2}$ and $R/{\cal J}\cong {\rm GF}(p^{r}),$ the finite field of $p^{r}$ elements, for any prime $p$ and any positive integer $r.$
DOI : 10.4064/cm111-1-9
Keywords: completely primary ring ring identity neq whose subset zero divisors forms unique maximal ideal cal determine structure group automorphisms aut completely primary finite ring characteristic cal jacobson radical cal cal neq annihilator cal coincides cal cal cong finite field elements prime positive integer

Chiteng'a John Chikunji 1

1 Department of Basic Sciences Botswana College of Agriculture P/BAG 0027, Gaborone, Botswana 
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Chiteng'a John Chikunji. Automorphisms of completely primary finite rings of
characteristic $p$. Colloquium Mathematicum, Tome 111 (2008) no. 1, pp. 91-113. doi: 10.4064/cm111-1-9

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