Geodesic
Varieties of representations of finite-dimensional algebras in prime algebras
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (1982), pp. 31-37 
Yu. P. Razmyslov. Varieties of representations of finite-dimensional algebras in prime algebras. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (1982), pp. 31-37. http://geodesic.mathdoc.fr/item/VMUMM_1982_6_a6/
@article{VMUMM_1982_6_a6,
     author = {Yu. P. Razmyslov},
     title = {Varieties of representations of finite-dimensional algebras in prime algebras},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {31--37},
     year = {1982},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_6_a6/}
}
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We prove that the pairs $(A_1,\mathfrak{G}_1)$ and $(A_2,\mathfrak{G}_2)$ have the same identical relations if and only if for some field extension $K_1\supset K$ the pairs $(K_1\otimes_K A_1,K_1\otimes_K\mathfrak{G}_1)$ and $(K_1\otimes_K A_2,K_1\otimes_K\mathfrak{G}_2)$ are semilinear isomorphic. Here $\mathfrak{G}_1$, $\mathfrak{G}_2$ are some finite dimensional $K$-algebras of signature $\Omega'$ and $A_1$, $A_2$ are some central prime algebras of signature $\Omega$.