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Die arithmetische Operation der Summe. (German) Zbl 0554.06007

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
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