On absorption in semigroups and $n$-ary semigroups

DOI10.2168/LMCS-11(2:15)2015zbMATH Open1326.08002arXiv1504.02899MaRDI QIDQ2941764

Bojan Bašić

Publication date: 25 August 2015

Published in: Logical Methods in Computer Science (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1504.02899

zbMATH Keywords

absorption\(n\)-ary semigroupsternary semigroupsidempotent terms

Mathematics Subject Classification ID

Applications of universal algebra in computer science (08A70) Finitary algebras (08A62) (n)-ary systems ((nge 3)) (20N15) Ternary systems (heaps, semiheaps, heapoids, etc.) (20N10)

Related Items (1)

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