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Categorical equivalence of clones of operations preserving a nontrivial $n$ $n$ -equivalence

Passawan Noppakaew

Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom 73000, Thailand

E-mail Address: noppakaew_p@silpakorn.edu

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and

Worakrit Supaporn

Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom 73000, Thailand

E-mail Address: supaporn_w@silpakorn.edu

Corresponding author.

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https://doi.org/10.1142/S1793557120500527Cited by:0 (Source: Crossref)

Abstract

In this paper, we showed that any clone of operations preserving a nontrivial $n$ $n$ -equivalence on a finite set is categorically equivalent to the clone of operations preserving a nontrivial $n$ $n$ -equivalence on a set having the cardinality of $3$ $3$ .

Communicated by J. Koppitz

Keywords:

AMSC: 08A40, 18B99, 06B23

References

1. K. Denecke and O. Lüders, Category equivalences of clones, Algebra Univer. 34 (1995) 608–618. Web of Science, Google Scholar
2. B. A. Davey and H. Werner, Dualities and equalities for varieties of algebras, Contributions to lattice theory, in Proc. Conf. Szeged, 1980 Colloq. Math. Soc. János Bolyai, North-Holland, Amsterdam, (1983), pp. 101–275. Google Scholar
3. J. Koppitz and W. Supaporn, Category equivalences of clones of operations preserving unary operations, C. R. Acad. Bulg Sci. 66(2) (2013) 177–184. Web of Science, Google Scholar
4. D. Lau, Function Algebras on Finite Sets, Springer Monograph in Mathematics (Germany, 2006). Google Scholar
5. R. McKenzie, An algebraic version of categorical equivalence for varieties and more general algebraic categories, in Logic and Algebra eds. A. Ursini and P. Agliano, (1996), pp. 211–243. Google Scholar
6. V. Novák and M. Novotnỳ, Pseudodimension of relational structures, Czech. Math. J. 49 (1999) 547–560. Web of Science, Google Scholar
7. R. Pöschel, Concrete representation of algebraic structures and a general Galois theory” Contributions to general algebra, in Proc. Klagenfurt Conf., Klagenfurt, 1978, Heyn, Klagenfurt, (1978), pp. 249–272. Google Scholar
8. R. Pöschel, A genaral Galois theory for operations and relations and concrete characterization of related algebraic structures, Akademie der Wissenschaften der DDR Institut für Mathematik Berlin, 1 (1980). Google Scholar
9. E. L. Post, The two-valued iterative systems of mathematical logic, Ann. Math. Studies 5 (1941) 122. Google Scholar
10. I. G. Rosenberg, Über die funktionale Vollständigkeit in den mehrwertigen Logiken. Struktur der Funktionen von mehreren Veränderlichen auf endlichen Mengen, Roz. Ces. Akad. Věd 80 (1970) 3–93. Google Scholar
11. J. Ušan and B. Šešelja, Transitive n-ary relations and characterizations of generalized equivalences, Univ. u Novom Sadu zb. Rad.Prirod.-Mat. Fak. Ser. Mat. 11 (1981) 231–245. Google Scholar

Vol. 12, No. 01

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History

Received 30 July 2018

Accepted 9 October 2018

Published: November 30, 2018

Information

This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited.

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Categorical equivalence of clones of operations preserving a nontrivial nn<math altimg="eq-00001.gif" display="inline"><mi>n</mi></math>-equivalence

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Categorical equivalence of clones of operations preserving a nontrivial $n$ $n$ -equivalence