\memo{[PRECEEDING STUDIES]}
The classification theorem of modulo riegs is proven in Burris and Lee's \cite{burris1993tarski}.
\url{https://math.stackexchange.com/questions/599172/structures-with-addition-multiplication-and-exponentiation}
\url{https://en.wikipedia.org/wiki/Tarski\%27s_high_school_algebra_problem}
\url{https://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/0896-09.pdf}
\url{https://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1476-17.pdf}
exponential rings
There is a survey paper on this topic: \cite{burris2005saga}.