(untitled) (European Journal of Pure and Applied Mathematics, 2025)
For any algebra of type τ, this paper introduces a novel class of terms (or terms) of a weakly fixed variable of type τ. Algebraic structures in sence of multisorted algebras are studied. In fact, it is shown that the set of such terms and the multisort operations forms a multisorted algebra that satisfies some axioms from the theory of clone. As a tool for classifying arbitrary algebras to subclasses called weakly fixed variable solid varieties, the seminearring of weakly fixed variable hypersubstitutions is proposed. Characterizations for any variety V of algebras of type τ to be a weakly fixed variable solid variety are explored.