N. L. Ackerman, A characterization of quasitrivial n-semigroups

M. Couceiro and J. Devillet, Every quasitrivial n-ary semigroup is reducible to a semigroup
URL : https://hal.archives-ouvertes.fr/hal-02099236

M. Couceiro, J. Devillet, and J. Marichal, Quasitrivial semigroups: characterizations and enumerations, Semigroup Forum, vol.98, issue.3, pp.472-498, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01826868

J. Devillet, G. Kiss, and J. Marichal, Characterizations of quasitrivial symmetric nondecreasing associative operations, Semigroup Forum, vol.98, pp.154-171, 2019.

W. A. Dudek and V. V. Mukhin, On n-ary semigroups with adjoint neutral element. Quasigroups and Related Systems, vol.14, pp.163-168, 2006.

W. Dörnte, Untersuchungenüber einen verallgemeinerten Gruppenbegriff, Math. Z, vol.29, pp.1-19, 1928.

G. Kiss and G. Somlai, Associative idempotent nondecreasing functions are reducible, Semigroup Forum, vol.98, pp.140-153, 2019.

E. Lehtonen and F. Starke, On associative operations on commutative integral domains. Semigroup Forum, 2019.

H. Länger, The free algebra in the variety generated by quasi-trivial semigroups, Semigroup Forum, vol.20, pp.151-156, 1980.

J. Marichal and P. Mathonet, A description of n-ary semigroups polynomial-derived from integral domains, Semigroup Forum, vol.83, pp.241-249, 2011.

E. L. Post, Polyadic groups, Trans. Amer. Math. Soc, vol.48, pp.208-350, 1940.

J. J. Rotman, An Introduction to the Theory of Groups, 1995.

Á. Szendrei, Clones in Universal Algebra, Séminaire de Mathématiques Supérieures, vol.99, 1986.

. Université-de-lorraine, . Cnrs, L. Inria, and F. Nancy, FRANCE Email address: miguel.couceiro[at]{inria,loria}.fr MATHEMATICS RESEARCH UNIT