The Degree of Invariancy of a Bicentrally Closed Clone
It is a fundamental fact of the theory of finite clones that every clone C on a set A can be described by the relations on A preserved by the operations in C. Some clones, called “bicentrally closed”, are completely determined by the finitary operations they preserve. In this paper we call attention to the smallest n (if it exists) such that C is characterized by its invariant operations of rank at most n, and look in particular at the clones with n = 1 and their associated algebras, i.e. the algebras whose term operations are precisely those preserved by every endomorphism. Although we are aware of the fragmentary and incomplete nature of the ideas and results presented here, we believe that communicating them at a conference will be helpful in testing their relevance.
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