Galois ring

Summary

A Galois ring is a finite commutative ring that extends $\Z/p^n\Z$ in the same way as a finite field $\F_{p^r}$ extends $\F_p$. Galois rings are local rings, and their residue fields are finite fields. They contain both the rings $\Z/p^n\Z$ and the finite fields as special cases. They are used in the theory of codes over $\Z/4\Z$ and in the study of finite rings.