Abstract
Let f : A → A be a self-map of the set A. We give a necessary and sufficient condition for the existence of a lattice structure (A, ∨, ∧) on A such that f becomes a lattice anti-endomorphism with respect to this structure.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Foldes S., Szigeti J.: Maximal compatible extensions of partial orders. J. Aust. Math. Soc. 81, 245–252 (2006)
Grätzer, G.: General Lattice Theory. Birkhauser, Basel (2003)
Jakubíková-Studenovská, D., Pócs, J.: Monounary Algebras. UPJŠ Košice (2009)
Jakubíkova-Studenovská D., Pöschel R., Radeleczki S.: The lattice of compatible quasiorders of acyclic monounary algebras. Order 28, 481–497 (2011)
Lengvárszky Zs.: Linear extensions of partial orders preserving antimonotonicity. Publ. Math. Debrecen 38, 279–285 (1991)
Szigeti J.: Maximal extensions of partial orders preserving antimonotonicity. Algebra Universalis 66, 143–150 (2011)
Szigeti J.: Which self-maps appear as lattice endomorphisms?. Discrete Math 321, 53–56 (2014)
Author information
Authors and Affiliations
Corresponding author
Additional information
Presented by J. Berman.
The second author was supported by OTKA K101515 and his research was carried out as part of the TAMOP-4.2.1.B-10/2/KONV-2010-0001 project with support by the European Union, co-financed by the European Social Fund.
Rights and permissions
About this article
Cite this article
Foldes, S., Szigeti, J. Which self-maps appear as lattice anti-endomorphisms?. Algebra Univers. 75, 439–449 (2016). https://doi.org/10.1007/s00012-015-0366-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00012-015-0366-8