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Title: | On absorption in semigroups and n-ary semigroups | Authors: | Bašić Bojan | Issue Date: | 2015 | Journal: | Logical Methods in Computer Science | Abstract: | © B. Bašić. 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. | URI: | https://open.uns.ac.rs/handle/123456789/31289 | ISSN: | 1860-5974 | DOI: | 10.2168/LMCS-11(2 |
Appears in Collections: | PMF Publikacije/Publications |
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