Coefficient subrings of certain local rings with prime-power characteristic

Abstract

If R is a local ring whose radical J(R) is nilpotent and R/J(R) is a commutative field which is algebraic over GF(p), then R has at least one subring S such that S=∪i=1∞Si, where each Si, is isomorphic to a Galois ring and S/J(S) is naturally isomorphic to R/J(R). Such subrings of R are mutually isomorphic, but not necessarily conjugate in R.