| Abstrakt: |
We study clones modulo minor homomorphisms, which are mappings from one clone to another preserving arities of operations and respecting permutation and identification of variables. Minor-equivalent clones satisfy the same sets of identities of the form f (x 1 , ⋯ , x n) ≈ g (y 1 , ⋯ , y m) , also known as minor identities, and therefore share many algebraic properties. Moreover, it was proved that the complexity of the CSP of a finite structure A only depends on the set of minor identities satisfied by the polymorphism clone of A . In this article we consider the poset that arises by considering all clones over a three-element set with the following order: we write C ⪯ m D if there exists a minor homomorphism from C to D . We show that the aforementioned poset has only three submaximal elements. [ABSTRACT FROM AUTHOR] |
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