$n$-Algebraic complete algebras, pseudodirect product and operator of algebraic closure on the subsets of universal algebras

It is given the definitions of an $n$-algebraic complete algebra and an $n$-algebraic completeness of the algebra which makes it possible to find algebraic closures of subsets of universal algebras. It is given the connection of the $n$-complitness of algebra with the operation of pseudodirect product of algebras.