Abstract
The functor Z in question associates to every semigroup S the semigroup ring Z(S) where Z is the ring of integers. We construct two more functors, one naturally equivalent to Z and one adjoint of Z . In relation to the functor Z , we also study the functor which to each ring R associates the usual embedding of R into a unitary ring. We consider the effect of the functor Z on such semigroup constructions as strong semilattices of semigroups, Rees matrix and Bruck semigroups. The paper concludes with certain commutativity property of Z with the translational hull in semigroups and rings.
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