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Article

Keywords:
direct product decomposition; convex isomorphisms; directed multilattices; directly indecomposable lattices; internal direct product decomposition; directed set; multilattice
Summary:
By applying the solution of the internal direct product decomposition we investigate the relations between convex isomorphisms and direct product decompositions of directed multilattices.
References:
[1] M. Benado: Sur la théorie de la divisibilité. Acad. R. P. Romine, Bul. Sti. Sect. Mat. Fiz. 6 (1954), 263-270. MR 0067089 | Zbl 0057.25301
[2] C. C. Chen M. K. Koh: On the lattice of convex sublattices of a finite lattice. Nanta Math. 5 (1972), 93-95. MR 0351934
[3] J. Hashimoto: On direct product decompositions of partially ordered sets. Annals of Math. 54 (1951), 315-318. DOI 10.2307/1969532 | MR 0043067
[4] J. Jakubík M. Kolibiar: On some properties of pairs of lattices. Czechoslov. Math. J. 4 (1954), 1-27. (In Russian.) MR 0065529
[5] M. Kolibiar: Intervals, convex sublattices and subdirect representations of lattices. Universal algebra and applications, Banach Center Publications, Vol. 9, Warszawa, 1980, pp. 335-339. DOI 10.4064/-9-1-335-339 | MR 0738826
[6] M. Kolibiar J. Lihová: Convex automorphisms of a lattice. Math. Slovaca, to appear. MR 1248975
[7] A. G. Kurosh: Group Theory. Third edition, Moskva, 1967. (In Russian.) Zbl 0189.30801
[8] V. I. Marmazeev: The lattice of convex sublattices of a lattice. Ordered sets and lattices No. 9, Saratov. Gos. Univ., Saratov, 1986, pp. 50-58. (In Russian.) MR 0957970 | Zbl 0711.06005
[9] V. I. Marmazeev: A group of automorphisms of the lattice of convex sublattices of a lattice. Vestsi Akad. Navuk BSSR, Ser. fiz. mat. navuk (1988), no. 6, 110-112. (In Russian, English summary.) MR 0984119
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