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uniquely complemented lattice; generalized Boolean algebra; direct product
In this paper we generalize a result of V. N. Salij concerning direct product decompositions of lattices which are complete and uniquely complemented.
[1] Dilworth R. P.: Lattices with unique complements. Trans. Amer. Math. Soc. 57 (1945) 123-154. DOI 10.1090/S0002-9947-1945-0012263-6 | MR 0012263 | Zbl 0060.06103
[2] Salij V. N.: On complete lattices with unique complements. XIII All-Union Algebraic Conference, Abstracts of lectures and reports. Gomel, 1975, pp. 191-192. (In Russian.)
[3] Salij V. N.: Regular elements in complete uniquely complemented lattices. Universal algebra and applications, Banach Center Publ. Vol. 9. Warsaw, 1982, pp. 15-19. DOI 10.4064/-9-1-15-19 | MR 0738797 | Zbl 0511.06005
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