Multisorted Algebras of Trees of a Weakly Fixed Variable
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i2.5835Keywords:
operation, multisorted set, endomorphism, semigroup, varietyAbstract
For any algebra of type $\tau$, this paper introduces a novel class of terms (or terms) of a weakly fixed variable of type $\tau$. 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 $\tau$ to be a weakly fixed variable solid variety are explored.
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