Abstract
J. -L. Loday introduced the notion of a dimonoid and constructed the free dimonoid. Cayley’s theorem for dimonoids states that every dimonoid is isomorphic to some transformation dimonoid. In this paper we propose another approach to constructing dimonoids which is based on using a semigroup operation. Several dimonoid-theoretical constructions are suggested, and it is shown that any dimonoid is isomorphically embedded into some dimonoid constructed from a semigroup. A similar result is obtained for dirings.
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Acknowledgements
The authors wish to express their thanks to the anonymous referee for useful remarks, comments and suggestions.
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Communicated by Mikhail V. Volkov.
Dedicated to Professor V. I. Sushchansky who passed away on 29th of October 2016.
