Die arithmetische Operation der Summe. (German) Zbl 0554.06007

Slatinský, Emil

Arch. Math., Brno 20, 9-20 (1984).

Let G be an ordered set and for each \(i\in G\) let \(M_ i\) be a lattice. Consider the system \(S=\{M_ i: i\in G\}\). The author investigates the following partially ordered sets which can be constructed from S: (i) the cardinal sum; (ii) the lexicographic sum; (iii) the ordinal sum (in the last case it is assumed that G is a chain). There are found necessary and sufficient conditions under which the results of these constructions are again lattices. Also, there are given necessary and sufficient conditions for an ordinal product of two ordered sets to be a lattice.

Reviewer: J.Jakubík

MSC:

06B05	Structure theory of lattices
06A06	Partial orders, general

Keywords:

partially ordered sets; cardinal sum; lexicographic sum; ordinal sum; lattices