Modular, Weakly distributive and Normal trellises
Shashirekha B. Rai, Prashantha Rao · Journal of Physics Conference Series · 2021
Abstract Psosets and trellises are generalizations of posets and lattices respectively. In fact, these notions are introduced independently by E. Fried and H. L. Skala. It is well known that a graph can be used to describe a partial order. In this paper, the concepts of modular, weakly distributive and normal trellises are introduced. We have proved that a trellis satisfying sheering property is modular. It is also proved that every strongly connected trellis is nonmodular. It is shown that every separating element of a trellis is modular and every modular element is weakly separating. Well-known result of M.H. Stone namely “Every maximal ideal of a distributive lattice is prime” is generalized to trellises. It is proved that a relatively complemented trellis is a lattice if and only if it is normal.