ALGEBRAS ASSIGNED TO TERNARY RELATIONS

作者:Chajda Ivan*; Kolarik Miroslav; Laenger Helmut
来源:Miscolc Mathematical Notes, 2013, 14(3): 827-844.
DOI:10.18514/mmn.2013.507

摘要

We show that to every centred ternary relation T on a set A there can be assigned (in a non-unique way) a ternary operation t on A such that the identities satisfied by (A;t) reflect relational properties of T. We classify ternary operations assigned to centred ternary relations and we show how the concepts of relational subsystems and homomorphisms are connected with subalgebras and homomorphisms of the assigned algebra (A;t). We show that for ternary relations having a non-void median can be derived so-called median-like algebras. (A;t) which become median algebras if the median M-T(a, b, c) is a singleton for all a, b, c is an element of A. Finally, we introduce certain algebras assigned to cyclically ordered sets.

  • 出版日期2013