Graph isomorphisms of semilattices. (English) Zbl 0563.06004

Kolibiar, M.

Contributions to general algebra 3, Proc. Conf., Vienna 1984, 225-235 (1985).

[For the entire collection see Zbl 0559.00002.]
All partially ordered sets dealt with in this paper are assumed to be of locally finite length. The author proves a theorem on graph isomorphism of semilattices which is analogous to a theorem on graph isomorphism of lattices proven by the reviewer [Czech. Math. J. 35(110), 188-200 (1985)]. Next, two theorems on graph isomorphism of semimodular lattices are established. In the first of these theorems a result of the reviewer [Math. Slovaca 35, 229-232 (1985)] is sharpened. The second theorem says that any graph isomorphism of semimodular lattices is given by a subdirect product diagram of their join semilattices.

Reviewer: J.Jakubík

MSC:

06A12	Semilattices
06C10	Semimodular lattices, geometric lattices

Keywords:

partially ordered sets; graph isomorphism of semilattices; semimodular lattices

Citations:

Zbl 0559.00002