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.

Résumé

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 $r.$

Détail

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