Coefficient subrings of certain local rings with prime-power characteristic (Q1895268)

The author proves that if \(R\) is a local ring whose radical \(J(R)\) is nilpotent and \(R/J(R)\) is a commutative field which is algebraic over \(\text{GF}(p)\) then \(R\) has at least one subring \(S\) such that \(S=\bigcup^\infty_{i=1} S_i\), where each \(S_i\) is isomorphic to a Galois ring and \(S/J(S)\) is naturally isomorphic to \(R/J(R)\). Such subrings \(S\) of \(R\) are mutually isomorphic, but not necessarily conjugate in \(R\).