A characterization theorem for weak varieties. (Q5932595)

The concept of mixed product of partial algebras is defined as a common generalization of two operators: weak subalgebras and products of partial algebras. The main result is that a class of partial algebras is a weak variety if and only if it is closed under formation of mixed products and closed homomorphic images. Let us remark that this is an improvement of a wrong result by \textit{H.\ Höft} [Algebra Univers. 3, 203--215 (1973; Zbl 0287.08003)].