Remarks on Zil'ber's results: On the simplicity of the representation of groups and rings (Q1109026)

\textit{B. I. Zil'ber} [Fundam. Math. 95, 173-188 (1977; Zbl 0363.02060)] shows that the simplicity of a group of finite Morley rank is preserved by elementary equivalence, and simple groups of finite Morley rank are uncountably categorical (moreover they are almost strongly minimal). Extending this the author shows with the same method that the simplicity (or irreducibility) of a representation of a connected group or ring over a group of finite Morley rank is preserved by elementary equivalence. He also proves that a simple ring of finite Morley rank is almost strongly minimal.