Abstract
The main problem of clone theory is to describe the clone lattice for a given basic set. For a two-element basic set this was resolved by E.L. Post, but for at least three-element basic set the full structure of the lattice is still unknown, and the complete description in general is considered to be hopeless. Therefore, it is studied by its substructures and its approximations. One of the possible directions is to examine k-ary parts of the clones and their mutual inclusions. In this paper we study k-ary parts of maximal clones, for \(k\geqslant 2,\) building on the already known results for their unary parts. It turns out that the poset of k-ary parts of maximal clones defined by central relations contains long chains.
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Acknowledgements
We thank to anonymous referees for their helpful comments. Special acknowledgements go to one of the referees who pointed out a missing case in the proof of Theorem 3.3, and suggested a way to fill this gap.
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Communicated by Presented by F. M. Schneider.
Dedicated to Reinhard Pöschel on the occasion of his 75th birthday.
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The authors gratefully acknowledge the financial support of the Ministry of Science, Technological Development and Innovation of the Republic of Serbia (Grants no. 451-03-66/2024-03/200125 and 451-03-65/2024-03/200125).
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Mašulović, D., Pech, M. On k-ary parts of maximal clones. Algebra Univers. 85, 21 (2024). https://doi.org/10.1007/s00012-024-00851-x
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DOI: https://doi.org/10.1007/s00012-024-00851-x