Article
Full entry |
PDF
(0.3 MB)
Feedback
Keywords:
Psoset; trellis; ideal; meet-translation; derivation
Psoset; trellis; ideal; meet-translation; derivation
Summary:
G. Szász, J. Szendrei, K. Iseki and J. Nieminen 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.
References:
[1] Fried, E.: Tournaments and nonassociative lattices. Ann. Univ. Sci. Budapest. Eotvos Sect. Math. 13 (1970), 151–164. MR 0321837
[2] Grätzer, G.: General Lattice Theory. Birkhauser Verlag, Basel, 1978. MR 0504338
[3] Harary, F.: Graph Theory. Addison-Wesley Series in Mathematics, Addison-Wesley, Reading, 1971. MR 0256911
[4] Iseki, K.: On endomorphism with fixed elements on algebra. Proc. Japan Acad. 40, 1964, 403. MR 0170839
[5] Nieminen, J.: Derivations and translations on lattices. Acta Sci. Math. 38 (1976), 359–363. MR 0429687 | Zbl 0344.06004
[6] Nieminen, J.: The lattice of translations on a lattice. Acta Sci. Math. 39 (1977), 109–113. MR 0441798 | Zbl 0364.06005
[7] Parameshwara Bhatta, S., Shashirekha, H.: A characterization of completeness for trellises. Algebra Universalis 44 (2000), 305–308. DOI 10.1007/s000120050189 | MR 1816026 | Zbl 1013.06003
[8] Skala, H. L.: Trellis theory. Algebra Universalis 1 (1971), 218–233. DOI 10.1007/BF02944982 | MR 0302523 | Zbl 0242.06003
[9] Skala, H. L.: Trellis Theory. Amer. Math. Soc., Providence, R.I., 1972. MR 0325474 | Zbl 0242.06004
[10] Szász, G.: Derivations of lattices. Acta Sci. Math. 36 (1975), 149–154. MR 0382090 | Zbl 0284.06001
[11] Szász, G., Szendrei, J.: Über die Translationen der Halbverbände. Acta. Sci. Math. 18 (1957), 44–47. MR 0087667 | Zbl 0078.02002
Search
Partner of