Finite Homogeneous Rings of Odd Characteristic

Publisher Summary This chapter discusses the finite homogeneous rings of odd characteristic. The classification of finite homogeneous rings of odd characteristic is based on the work of Berline and Cherlin. R denotes a QE ring of characteristic p n where p is an odd prime and n ≥ 1 and J denotes its Jacobson radical. A countable ring R is homogeneous if every isomorphism between finitely generated subrings of R extends to an automorphism of R. The classification of all quantifier-eliminable (QE) rings is reduced to the classification of the Jacobson radicals of such rings. By assuming finiteness (QE is equivalent to homogeneous), all possible radicals for the characteristic p 2 case are listed, p an odd prime.