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Role of associativity in Ramsey algebras

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Abstract

It is known that semigroups are Ramsey algebras. This paper is an attempt to understand the role associativity plays in a binary system being a Ramsey algebra. Specifically, we show that the nonassociative Moufang loop of octonions is not a Ramsey algebra.

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Acknowledgements

This work grows out of Zu Yao Teoh’s research in the doctoral program at Universiti Sains Malaysia. The second and third authors gratefully acknowledge the support of the Fundamental Research Grant Scheme No. 203/PMATHS/6711464 of the Ministry of Education, Malaysia, and Universiti Sains Malaysia. Special thanks also go to the School of Mathematical Sciences’ postgraduate allocation fund of Universiti Sains Malaysia as well as the Centre International de Mathématiques Pures et Appliquées (CIMPA) for their financial supports in making attending the AMC 2016 possible for Zu Yao Teoh.

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Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, USM, Malaysia

    Andrew Rajah, Wen Chean Teh & Zu Yao Teoh

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  1. Andrew Rajah
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  2. Wen Chean Teh
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  3. Zu Yao Teoh
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Correspondence to Wen Chean Teh.

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Communicating Editor: B Sury

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Rajah, A., Teh, W.C. & Teoh, Z.Y. Role of associativity in Ramsey algebras. Proc Math Sci 127, 769–778 (2017). https://doi.org/10.1007/s12044-017-0359-y

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  • DOI: https://doi.org/10.1007/s12044-017-0359-y

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