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On order polynomially complete lattices. (English) Zbl 0784.06004
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)

06B05 Structure theory of lattices
08A40 Operations and polynomials in algebraic structures, primal algebras
Full Text: DOI
[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
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