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Keywords:
pseudo-ordered set; trellis; $p$-chain; ascending well-ordered $p$-chain; cycle-complete trellis; complete trellis
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:
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[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
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[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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