References
K. Varadarajn, “Dual Goldie dimension,” Commn. Algebra,7, No. 6, 565–610 (1979).
G. Gratzer, General Lattice Theory, Birkhauser, Basel (1978).
P. Grzeszczuk and E. R. Puczylowski, “On Goldie and dual Goldie dimensions,” J. Pure Appl. Algebra,31, Nos. 1–3, 47–54 (1984).
M. K. Bennett and G. Birkhoff, “Convexity lattices,” Algebra Univ.,20, No. 1, 1–26 (1985).
A. P. Zolotarev, “On Eckhoff's inequality in lattices with zero,” Sib. Mat. Zh.,31, No. 6, 217 (1990).
A. P. Zolotarev, “On Helly and Radon numbers in distributive lattices and in lattices with pseudocomplements,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 41–47 (1990).
A. P. Zolotarev, “On the Helly, Radon, and Carathéodory numbers in modular and atomic semimodular lattices,” in: Ordered Sets and Lattices [in Russian], Vol. 10 Saratov (1991), pp. 31–40.
G. Richter, “The Kuroš-Ore theorem, finite and infinite decompositions,” Studia Sci. Math. Hung.,17, Nos. 1–4, 243–250 (1982).
L. A. Skornyakov, Elements of Lattice Theory [in Russian], Nauka, Moscow (1970).
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Translated from Matematicheskie Zametki, Vol. 54, No. 3, pp. 34–39, September, 1993.
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Zolotarev, A.P. On the dual Helly number and irreducible decompositions of the unit in lattices. Math Notes 54, 899–902 (1993). https://doi.org/10.1007/BF01209554
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DOI: https://doi.org/10.1007/BF01209554