Abstract
Let A be an algebra. We say that the functions f 1, . . . , f m : A n → A are algebraic on A provided there is a finite system of term-equalities \({{\bigwedge t_{k}(\overline{x}, \overline{z}) = s_{k}(\overline{x}, \overline{z})}}\) satisfying that for each \({{\overline{a} \in A^{n}}}\), the m-tuple \({{(f_{1}(\overline{a}), \ldots , f_{m}(\overline{a}))}}\) is the unique solution in A m to the system \({{\bigwedge t_{k}(\overline{a}, \overline{z}) = s_{k}(\overline{a}, \overline{z})}}\). In this work we present a collection of general tools for the study of algebraic functions, and apply them to obtain characterizations for algebraic functions on distributive lattices, Stone algebras, finite abelian groups and vector spaces, among other well known algebraic structures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Balbes R., Dwinger P.: Distributive Lattices. University of Missouri Press, Columbia, Missouri (1974)
Campercholi M.: ‘Algebraically expandable classes of implication algebras’. Int. J. Algebra Comput. 20(5), 605–617 (2010)
Campercholi M., Vaggione D.: ‘Algebraically expandable classes’. Algebra Universalis 61(2), 151–186 (2009)
Czelakowski J., Dziobiak W.: ‘Congruence distributive quasivarieties whose finitely subdirectly irreducible members form a universal class’. Algebra Universalis 27(1), 128–149 (1990)
Gramaglia H., Vaggione D.J.: ‘Birkhoff-like sheaf representation for varieties of lattice expansions’. Studia Logica 56(1-2), 111–131 (1996)
Volger H.: ‘Preservation theorems for limits of structures and global sections of sheaves of structures’. Math. Z. 166, 27–54 (1979)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Campercholi, M., Vaggione, D. Algebraic Functions. Stud Logica 98, 285–306 (2011). https://doi.org/10.1007/s11225-011-9334-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11225-011-9334-2