Abstract
The unification type of a variety is a rough measure of the extent to which systems of equations in the free algebras of the variety have general solutions. We prove, using a concrete characterization of categorically equivalent varieties due to McKenzie, that categorically equivalent varieties have the same unification type.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Albert, M. H. andLawrence, J.,Unification in varieties of groups I: nilpotent groups. Canadian Journal of Mathematics,46 (1994), 1135–1149.
Albert, M. H. andWillard, R.,Unification in locally finite varieties, preprint 1992.
Burris, S. andSankappanavar, H. P.,A Course in Universal Algebra, Springer-Verlag, New York, 1981.
Nipkow, T.,Unification in primal algebras, their powers and their varieties, J.A.C.M.,37 (1990), 742–776.
MacLane, S.,Categories for the Working Mathematician, Springer-Verlag, New York, 1971.
McKenzie, R.,Algebraic Morita theorem for varieties, preprint, August 1992.
McKenzie, R., McNulty, G. andTaylor, W.,Algebras, Lattices, Varieties, Wadsworth/Brooks-Cole, Monterrey, 1987.
Siekmann, J.,Unification theory, J. Symbolic Computation,7 (1989), 207–274.
Taylor, W.,The fine spectrum of a variety, Algebra Universalis,5 (1975), 263–303.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Albert, M.H. Category equivalence preserves unification type. Algebra Universalis 36, 457–466 (1996). https://doi.org/10.1007/BF01233916
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01233916