Geodesic
The structure of models and a~decidability criterion for complete theories of finite-dimensional algebras
Izvestiya. Mathematics , Tome 34 (1990) no. 2, pp. 389-407.

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The author gives an algebraic description of models of the theory $\operatorname{Th}(R)$ and a criterion for its decidability for an arbitrary (not necessarily associative, and possibly without an identity) finite-dimensional $k$-algebra over a field $k$ of arbitrary characteristic. This description is based on the solution of the following purely algebraic problem: how completely can the structure of a $k$-module $R$ be recovered, knowing only the ring operations of $R$? Bibliography: 20 titles. 
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A. G. Myasnikov. The structure of models and a~decidability criterion for complete theories of finite-dimensional algebras. Izvestiya. Mathematics , Tome 34 (1990) no. 2, pp. 389-407. http://geodesic.mathdoc.fr/item/IM2_1990_34_2_a8/

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