Mathematica Bohemica, Vol. 141, No. 1, pp. 91-98, 2016
An ordered structure of pseudo- BCI-algebras
Ivan Chajda, Helmut Länger
Abstract: In Chajda's paper (2014), to an arbitrary BCI-algebra the author assigned an ordered structure with one binary operation which possesses certain antitone mappings. In the present paper, we show that a similar construction can be done also for pseudo-BCI-algebras, but the resulting structure should have two binary operations and a set of couples of antitone mappings which are in a certain sense mutually inverse. The motivation for this approach is the well-known fact that every commutative BCK-algebra is in fact a join-semilattice and we try to obtain a similar result also for the non-commutative case and for pseudo-BCI-algebras which generalize BCK-algebras, see e.g. Imai and Iseki (1966) and Iseki (1966).
Affiliations: Ivan Chajda, Department of Algebra and Geometry, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, CZ-771 46 Olomouc, Czech Republic, e-mail: ivan.chajda@upol.cz; Helmut Länger, Institute of Discrete Mathematics and Geometry, Faculty of Mathematics and Geoinformation, Vienna University of Technology, Wiedner Hauptstraße 8-10/104, A-1040 Vienna, Austria, e-mail: helmut.laenger@tuwien.ac.at
