Abstract:An n-tuple semigroup is an algebra defined on a set with n binary associative operations. This notion was considered by Koreshkov in the context of the theory of n-tuple algebras of associative type. The n>1 pairwise interassociative semigroups give rise to an n-tuple semigroup. This paper is a survey of recent developments in the study of free objects in the variety of n-tuple semigroups. We present the constructions of the free n-tuple semigroup, the free commutative n-tuple semigroup, the free rectangula… Show more
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