Abstract
In this paper we introduce a lattice construction, calledmultipasting, which is a common generalization of gluing, pasting, andS-glued sums. We give a Characterization Theorem which generalizes results for earlier constructions. Multipasting is too general to prove the analogues of many known results. Therefore, we investigate in some detail three special cases: strong multipasting, multipasting of convex sublattices, and multipasting with the Interpolation Property.
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Day, A. andHerrmann, Ch.,Gluings of modular lattices, Order5 (1988), 85–101.
Day, A. andJezek, J.,The Amalgamation Property for varieties of lattices, Trans. Amer. Math. Soc.286 (1984), 251–256.
Fried, E. andGrätzer, G.,Partial and free weakly associative lattices, Houston J. Math.24 (1976), 501–512.
Fried, E. andGrätzer, G.,Pasting and modular lattices, Proc. Amer. Math. Soc.196 (1989), 885–890.
Fried, E. andGrätzer, G.,Pasting infinite lattices, J. Austral. Math. Soc. (Series A)47 (1989), 1–21.
Fried, E. andGrätzer, G.,The Unique Amalgamation Property for lattices, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. (1990).
Fried, E. Grätzer, G., andLakser, H.,Projective geometries as cover preserving sublattices, Algebra Universalis27 (1990), 270–278.
Grätzer, G.,General Lattice Theory, Academic Press, New York, N.Y.; Birkhäuser Verlag, Basel; Akademie Verlag, Berlin, 1978.
Hall, M. andDilworth, R. P.,The embedding problem for modular lattices, Ann. of Math.2 (1944), 450–456.
Herrmann, Ch.,S-verklebte Summen von Verbänden, Math. Z.130 (1973), 255–274.
Slavík, V.,A note on the amalgamation properties in lattice varieties, Comm. Math. Univ. Carolinae21 (1980), 473–478.
Schmidt, E. T.,On splitting modular lattices, Colloquia Mathematica Soc. János Bólyai29 (1977), 697–703.
Schmidt, E. T.,On finitely projected modular lattices, Acta Math. Acad. Sci. Hungar.39 (1981), 45–51.
Schmidt, E. T.,On locally order-polynomially complete modular lattices, Acta Math. Acad. Sci. Hungar.49 (1987), 481–486.
Schmidt, E. T.,Pasting and semimodular lattices, Algebra Universalis27 (1990), 595–596.
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The research of the first and the third authors was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1813. The research of the second author was supported by the NSERC of Canada.
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Fried, E., Grätzer, G. & Schimidt, E.T. Multipasting of lattices. Algebra Universalis 30, 241–261 (1993). https://doi.org/10.1007/BF01196095
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DOI: https://doi.org/10.1007/BF01196095