Distributive, standard and neutral elements in trellises
Acta mathematica Universitatis Comenianae, Tome 77 (2008) no. 2
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In this paper, the concepts of distributive, standard and neutral elements introduced in lattices by O. Ore, G. Grätzer and G. Birkhoff, respectively, have been extended to trellises (also called weakly associative lattices) and some of their analogous characterizations are obtained. Also, the concept of a normal trellis is introduced as a generalization of a lattice and it is proved that an element d of a normal trellis L is neutral if and only if for any x, y Î L , the elements d, x, y generate a distributive subtrellis of L .