Bašić, Bojan - On absorption in semigroups and $n$-ary semigroups

lmcs:1575 - Logical Methods in Computer Science, June 25, 2015, Volume 11, Issue 2
On absorption in semigroups and $n$-ary semigroups

Authors: Bašić, Bojan

The notion of absorption was developed a few years ago by Barto and Kozik and immediately found many applications, particularly in topics related to the constraint satisfaction problem. We investigate the behavior of absorption in semigroups and n-ary semigroups (that is, algebras with one n-ary associative operation). In the case of semigroups, we give a simple necessary and sufficient condition for a semigroup to be absorbed by its subsemigroup. We then proceed to n-ary semigroups, where we conjecture an analogue of this necessary and sufficient condition, and prove that the conjectured condition is indeed necessary and sufficient for B to absorb A (where A is an n-ary semigroup and B is its n-ary subsemigroup) in the following three cases: when A is commutative, when |A-B|=1 and when A is an idempotent ternary semigroup.

Source : oai:arXiv.org:1504.02899
DOI : 10.2168/LMCS-11(2:15)2015
Volume: Volume 11, Issue 2
Published on: June 25, 2015
Submitted on: June 16, 2014
Keywords: Computer Science - Logic in Computer Science