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Article

Bhatta, S. Parameshwara ; Shashirekha, H.
Some characterizations of completeness for trellises in terms of joins of cycles. (English). Czechoslovak Mathematical Journal, vol. 54 (2004), issue 1, pp. 267-272
MSC: 06A06, 06B05 | MR 2040239 | Zbl 1049.06004
Keywords:
pseudo-ordered set; trellis; $p$-chain; ascending well-ordered $p$-chain; cycle-complete trellis; complete trellis
Summary:
This paper gives some new characterizations of completeness for trellises by introducing the notion of a cycle-complete trellis. One of our results yields, in particular, a characterization of completeness for trellises of finite length due to K. Gladstien (see K. Gladstien: Characterization of completeness for trellises of finite length, Algebra Universalis 3 (1973), 341–344).
References:
[1] P.  Crawley and R. P.  Dilworth: Algebraic Theory of Lattices. Prentice Hall, Inc., Englewood Cliffs, 1973.
[2] E.  Fried: Tournaments and non-associative lattices. Ann. Univ. Sci. Budapest, Sect. Math. 13 (1970), 151–164. MR 0321837
[3] E.  Fried and G.  Gratzer: Some examples of weakly associative lattices. Colloq. Math. 27 (1973), 215–221. DOI 10.4064/cm-27-2-215-221 | MR 0327590
[4] K.  Gladstien: A characterization of complete trellises of finite length. Algebra Universalis 3 (1973), 341–344. DOI 10.1007/BF02945138 | MR 0349502 | Zbl 0318.06002
[5] S.  Parameshwara Bhatta and H.  Shashirekha: A characterization of completeness for trellises. Algebra Universalis 44 (2000), 305–308. DOI 10.1007/s000120050189 | MR 1816026
[6] H. L.  Skala: Trellis theory. Algebra Universalis 1 (1971), 218–233. DOI 10.1007/BF02944982 | MR 0302523 | Zbl 0242.06003
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