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On associative operations on commutative integral domains

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We describe the associative multilinear polynomial functions over commutative integral domains. This extends Marichal and Mathonet’s result on infinite integral domains and provides a new proof of Andres’s classification of two-element n-semigroups.

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  1. Andres, S.D.: Classification of all associative mono-\(n\)-ary algebras with 2 elements. Int. J. Math. Math. Sci. 2009, Article ID 678987, 16 pages (2009)

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The authors would like to thank Robert Baumann, Thomas Quinn-Gregson, and Nikolaas Verhulst for inspiring discussions and the anonymous reviewer for helpful comments.

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Correspondence to Erkko Lehtonen.

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Communicated by Jorge Almeida.

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Lehtonen, E., Starke, F. On associative operations on commutative integral domains. Semigroup Forum 100, 910–915 (2020).

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