On the $\gamma$-classical varieties

We study a $\gamma$-classical varieties of associative algebras with trace. They were introduced by A. R. Kemer. It is proven that in case of characteristic $p>0$ there exists only a finite number of minimal $\gamma$-classical varieties. The basises of identities of these varieties are described. We also consruct new examples of prime varieties in positive characteristic using a new notion of convolution.