On some algorithmic problems and free products in $R$-varieties of linear $\Omega$-algebras

A new method for investigation of linear $\Omega$-algebras is suggest. This method based on the original definition of partial linear $\Omega$-algebra. The method is effective for varieties with analog of Evans's embedding theorem. In the present paper a family of such varieties is defined. For these varieties the positive solution of wordproblem and subalgebraproblem is obtained and the theory of free algebras and free products of algebras is developed. In particular results of this paper generalise some known results of other authors.