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Automorphisms of completely primary finite rings of characteristic p

Chiteng'a John Chikunji (2008)

Colloquium Mathematicae

A completely primary ring is a ring R with identity 1 ≠ 0 whose subset of zero-divisors forms the unique maximal ideal . We determine the structure of the group of automorphisms Aut(R) of a completely primary finite ring R of characteristic p, such that if is the Jacobson radical of R, then ³ = (0), ² ≠ (0), the annihilator of coincides with ² and R / G F ( p r ) , the finite field of p r elements, for any prime p and any positive integer r.

Automorphisms of models of bounded arithmetic

Ali Enayat (2006)

Fundamenta Mathematicae

We establish the following model-theoretic characterization of the fragment IΔ₀ + Exp + BΣ₁ of Peano arithmetic in terms of fixed points of automorphisms of models of bounded arithmetic (the fragment IΔ₀ of Peano arithmetic with induction limited to Δ₀-formulae). Theorem A. The following two conditions are equivalent for a countable model of the language of arithmetic: (a) satisfies IΔ₀ + BΣ₁ + Exp; (b) = I f i x ( j ) for some nontrivial automorphism j of an end extension of that satisfies IΔ₀. Here I f i x ( j ) is the...

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