Automorphisms of completely primary finite rings of characteristic p

• Autorzy: Chiteng'a John Chikunji
• Języki publikacji: EN

Abstrakty

EN

A completely primary ring is a ring R with identity 1 ≠ 0 whose subset of zero-divisors forms the unique maximal ideal 𝒥. We determine the structure of the group of automorphisms Aut(R) of a completely primary finite ring R of characteristic p, such that if 𝒥 is the Jacobson radical of R, then 𝒥³ = (0), 𝒥² ≠ (0), the annihilator of 𝒥 coincides with 𝒥² and $R/𝒥 ≅ {GF}(p^{r})$, the finite field of $p^{r}$ elements, for any prime p and any positive integer r.

Kategorie tematyczne

• 16P10: Finite rings and finite-dimensional algebras
• 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures
• 16L99: None of the above, but in this section
• 12E20: Finite fields (field-theoretic aspects)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 111
• Numer: 1
• Strony: 91-113

Daty

wydano

2008

Twórcy

autor

Chiteng'a John Chikunji

• Department of Basic Sciences, Botswana College of Agriculture, P/BAG 0027, Gaborone, Botswana

Identyfikatory

DOI

10.4064/cm111-1-9