Green's Relation R on the Monoid of Clone Endomorphisms

• 来源期刊: 代数集刊(英文版)
• 关键词: hypersubstitutions transformation semigroups Green's relations
• 年，卷（期）: 2005,（3）
• 页码范围: 519-530
• 页数: 12页
• 语种: 英文

摘要

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.