【摘 要】
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A hypersubstitution is a map which takes n-ary operation symbols to n-ary terms. Any such map can be uniquely extended to a map defined on the set Wτ(X)of all
【机 构】
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Universit(a)t Potsdam, Institut für Mathematik D-14415 Potsdam, Germany
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A hypersubstitution is a map which takes n-ary operation symbols to n-ary terms. Any such map can be uniquely extended to a map defined on the set Wτ(X)of all terms of type τ, and any two such extensions can be composed in a natural way.Thus, the set Hyp(τ) of all hypersubstitutions of type τ forms a monoid. In this paper,we characterize Green’s relation R on the monoid Hyp(τ) for the type τ = (n, n). In this case, the monoid of all hypersubstitutions is isomorphic with the monoid of all clone endomorphisms. The results can be applied to mutually derived varieties.
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