Kaiser, H. K.; Sauer, N. On order polynomially complete lattices. (English) Zbl 0784.06004 Algebra Univers. 30, No. 2, 171-176 (1993). It is proven that every order polynomially complete lattice is bounded. Hence, a polynomially complete lattice cannot be countably infinite. This partially solves one of the most famous problems in the theory of polynomially complete lattices. However, the problem remains open for the uncountable case. Reviewer: I.Chajda (Přerov) Cited in 2 Documents MSC: 06B05 Structure theory of lattices 08A40 Operations and polynomials in algebraic structures, primal algebras Keywords:infinite lattice; order polynomially complete lattice PDF BibTeX XML Cite \textit{H. K. Kaiser} and \textit{N. Sauer}, Algebra Univers. 30, No. 2, 171--176 (1993; Zbl 0784.06004) Full Text: DOI References: [1] Dorninger, D.,A note on local polynomial functions over lattices. Algebra Universalis11, 135-138 (1980). · Zbl 0453.08002 · doi:10.1007/BF02483091 [2] Dorninger, D.,On generating sets of order-preserving functions over finite lattices. Coll. Math. Soc. J. Bolyai33, 317-324 (1980). [3] Gr?tzer, G.,Lattice Theory. Freeman and Company, San Francisco, 1971. [4] Kindermann, M.,?ber die ?quivalenz von Ordnungspolynomvollst?ndigkeit und Toleranzeinfachheit endlicher Verb?nde. Contributions to General Algebra2, 145-149 (1979). [5] Schweigert D.,?ber endliche, ordnungspolynomvollst?ndige Verb?nde. Monatsh. f. Math.78, 68-76 (1974). · Zbl 0287.06004 · doi:10.1007/BF01298196 [6] Wille, R.,Ein Charakterisierung endlicher ordnungspolynomvollst?ndiger Verb?nde. Arch. d. Math.28, 557-560 (1972). · Zbl 0357.06006 · doi:10.1007/BF01223966 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.