Abstract
A stronger version of a known property is shown to hold for the natural equaclosure operator on subquasivariety lattices.
Similar content being viewed by others
References
Adaricheva, K.: On the prevariety of perfect lattices. Algebra Univ. 65, 21–39 (2011)
Adaricheva, K., Gorbunov, V:: Equational closure operator and forbidden semidistributive lattices. Sib. Math. J. 30, 831–849 (1989)
Adaricheva, K., Hyndman, J., Nation, J., Nishida, J.: A primer of quasivariety lattices. Draft. http://math.hawaii.edu/~jb/
Adaricheva, K., Nation, J.: Lattices of quasi-equational theories as congruence lattices of semilattices with operators, Parts I and II. Int. J. Algebra Comput. 22, N7 (2012)
Adaricheva, K., Nation, J.: Lattices of algebraic subsets and implicational classes. In: Grätzer, G., Wehrung, F. (eds.) Lattice Theory: Special Topics and Applications, vol. 2, pp. 103–151. Birkhäuser/Springer, Cham (2016)
Dziobiak, W.: On atoms in the lattice of quasivarieties. Algebra Univ. 24, 32–35 (1987)
Gorbunov, V.: Algebraic Theory of Quasivarieties. Plenum, New York (1998)
Hoehnke, H.-J.: Fully invariant algebraic closure systems of congruences and quasivarieties of algebras. In: Lectures in Universal Algebra (Szeged, 1983), Colloq. Math. Soc. János Bolyai, vol. 43, pp. 189–207. North-Holland, Amsterdam (1986)
Hyndman, J., Nation, J., Nishida, J.: Congruence lattices of semilattices with operators. Studia Logica 104, 305–316 (2016)
Nation, J.: Lattices of theories in languages without equality. Notre Dame J. Form. Log. 54, 167–175 (2013)
Tumanov, V.: Finite distributive lattices of quasivarieties. Algebra Logic 22, 119–129 (1983)
Author information
Authors and Affiliations
Corresponding author
Additional information
In memory of E. Tamás Schmidt.
This article is part of the topical collection “In memory of E. Tamás Schmidt” edited by Robert W. Quackenbush.
Rights and permissions
About this article
Cite this article
Nation, J.B., Nishida, J. A refinement of the equaclosure operator. Algebra Univers. 79, 46 (2018). https://doi.org/10.1007/s00012-018-0518-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00012-018-0518-8