caa a22 4500 445345136 CHVBK 20180317142826.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00233-011-9313-y doi (NATIONALLICENCE)springer-10.1007/s00233-011-9313-y Finite degree: algebras in general and semigroups in particular [Elektronische Daten] [B. Davey, M. Jackson, J. Pitkethly, C. Szabó] An algebra A has finite degree if its term functions are determined by some finite set of finitary relations onA. We study this concept for finite algebras in general and for finite semigroups in particular. For example, we show that every finite nilpotent semigroup has finite degree (more generally, every finite algebra with bounded p n -sequence), and every finite commutative semigroup has finite degree. We give an example of a five-element unary semigroup that has infinite degree. We also give examples to show that finite degree is not preserved in general under taking subalgebras, homomorphic images, direct products or subdirect factors. Springer Science+Business Media, LLC, 2011 Semigroup nationallicence Term functions nationallicence Clone nationallicence Finite degree nationallicence Finitely related nationallicence Davey B. Department of Mathematics and Statistics, La Trobe University, 3086, Victoria, Australia aut Jackson M. Department of Mathematics and Statistics, La Trobe University, 3086, Victoria, Australia aut Pitkethly J. Department of Mathematics and Statistics, La Trobe University, 3086, Victoria, Australia aut Szabó C. Department of Algebra and Number Theory, Eötvös University, 1117, Budapest, Hungary aut Semigroup Forum Springer-Verlag 83/1(2011-08-01), 89-110 0037-1912 83:1<89 2011 83 233 https://doi.org/10.1007/s00233-011-9313-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-011-9313-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Davey B. Department of Mathematics and Statistics, La Trobe University, 3086, Victoria, Australia aut NATIONALLICENCE 700 1- Jackson M. Department of Mathematics and Statistics, La Trobe University, 3086, Victoria, Australia aut NATIONALLICENCE 700 1- Pitkethly J. Department of Mathematics and Statistics, La Trobe University, 3086, Victoria, Australia aut NATIONALLICENCE 700 1- Szabó C. Department of Algebra and Number Theory, Eötvös University, 1117, Budapest, Hungary aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 83/1(2011-08-01), 89-110 0037-1912 83:1<89 2011 83 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer