Abstract
An n-tuple semigroup is an algebra defined on a set with n binary associative operations. This notion play a prominent role in the theory of n-tuple algebras of associative type. Our paper is devoted to the development of the variety theory of n-tuple semigroups. We construct a free k-nilpotent n-tuple semigroup and characterize the least k-nilpotent congruence on a free n-tuple semigroup.
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