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Derivations and translations on trellises. (English) Zbl 1350.06004

Summary: G. Szasz and J. Szendrei [Acta Sci. Math. 18, 44–47 (1957; Zbl 0078.02002)], G. Szasz [Acta Sci. Math. 37, 149–154 (1975; Zbl 0284.06001)], K. Iseki [Proc. Japan Acad. 40, 403 (1964; Zbl 0161.01406)] and J. Nieminen [Acta Sci. Math. 38, 359–363 (1976; Zbl 0344.06004); Acta Sci. Math. 39, 109–113 (1977; Zbl 0364.06005)] have made an extensive study of derivations and translations on lattices. In this paper, the concepts of meet-translations and derivations have been studied in trellises (also called weakly associative lattices or WA-lattices) and several results in lattices are extended to trellises. The main theorem of this paper, namely, that every derivatrion of a trellis is a meet-translation, is proved without using associativity and it generalizes a well-known result of G. Szász [loc. cit.].

MSC:

06B05 Structure theory of lattices
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