Tardos, Gábor A maximal clone of monotone operations which is not finitely generated. (English) Zbl 0614.08006 Order 3, 211-218 (1986). A set of finitary operations on a finite set A is called a clone on A if it contains all projections and is closed under superposition. In his paper [Rozpr. Česk. Akad. Věd., Řada Mat. Přír. Věd. 80, No.4, 3-93 (1970; Zbl 0199.302)], I. G. Rosenberg classified the maximal clones. In the paper [Z. Math. Logik Grundl. Math. 24, 79-96 (1978; Zbl 0401.03008)] by D. Lau, it has been shown that for \(| A| \leq 7\) every maximal clone on A is finitely generated. In the present paper, the author studies a maximal clone on a set of eight elements and proves, that this clone - which consists of all finitary operations preserving a certain partial order - is not finitely generated. Since it is already known that all other maximal clones on an eight element set are finitely generated, this result settles the case \(| A| =8\). Reviewer: G.Eigenthaler Cited in 1 ReviewCited in 20 Documents MSC: 08A40 Operations and polynomials in algebraic structures, primal algebras 06A06 Partial orders, general Keywords:maximal clones; finitely generated; finitary operations; partial order Citations:Zbl 0199.302; Zbl 0401.03008 PDFBibTeX XMLCite \textit{G. Tardos}, Order 3, 211--218 (1986; Zbl 0614.08006) Full Text: DOI References: [1] K. A. Baker and A. F. Pixley (1975) Polynomial interpolations and the Chinese remainder theorem for algebraic systems, Math. Z. 143, 165-174. · Zbl 0298.08004 · doi:10.1007/BF01187059 [2] J. Demetrovics, L. Hann?k, and L. Ronyai (1984) Near unanimity functions and partial orderings, Proc. 14, ISMVL., Manitoba, pp. 52-56. [3] D. Lau (1978) Bestimmung der Ordnung maximaler Klassen von Funktionen der k-wertigen Logik. Z. Math. Logik u. Grundl. Math. 24, 79-96. · Zbl 0401.03008 · doi:10.1002/malq.19780240111 [4] R. P?schel and L. A. Kalu?nin (1979) Funktionen-und Relationenalgebren, VEB Deutscher Verlag der Wissenschaften, Berlin. [5] I. G. Rosenberg (1970) ?ber die funktionale Vollstandigkeit in den mehrwertigen Logiken, Rozpr. ?SAV ?ada Mat. P?ir. V?d. 80, 4, 3-93. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.