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Affine complete distributive lattices. (English) Zbl 0816.06010
Summary: We prove a characterization theorem for affine complete distributive lattices. To do so we introduce the notions of almost principal ideal and almost principal filter.

06D99 Distributive lattices
08A40 Operations and polynomials in algebraic structures, primal algebras
Full Text: DOI
[1] D. Dorninger and G. Eigenthaler (1982)On Compatible and Order-Preserving Functions, Universal Algebra and Applications, vol. 9, Banach Center Publications, Warsaw, pp. 97–104. · Zbl 0511.08002
[2] G. Grätzer (1964) Boolean functions on distributive lattices,Acta Math. Acad. Sci. Hung. 15, 195–201. · Zbl 0146.01902
[3] D. Schweigert (1974) Über endliche, ordnungspolynomvollständige Verbände,Monatsh. Math. 78, 68–76. · Zbl 0287.06004
[4] H. Werner (1971) Produkte von Kongruenzklassengeometrien universeller Algebren,Math. Z. 121, 111–140. · Zbl 0203.22902
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