Automorphisms and model-theory questions for nilpotent matrix groups and rings

Let $R'=\mathrm{NT}(m, S)$. The purpose of the paper is the investigation of elementary equivalences $\mathrm{UT}(n,K)\equiv\mathrm{UT}(m,S)$ and $\Lambda(R)\equiv\Lambda(R')$ for arbitrary associative coefficient rings with identity. The main theorem gives the description of such equivalences for $n>4$. In addition, we investigate isomorphisms and elementary equivalence of Jordan niltriangular matrix rings.