Multisorted Algebras of Trees of a Weakly Fixed Variable (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.