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Modular incidence structures. (Modulare Inzidenzstrukturen.) (German) Zbl 0853.08001

Summary: Modular incidence structures are defined and are shown to be, as ordered sets, modular in the sense of J. Larmerová and J. Rachůnek [Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 91, Math. 27, 13-23 (1988; Zbl 0693.06003)]. Some fundamental properties of modular incidence structures are deduced and some examples of such structures are presented.

MSC:

08A02 Relational systems, laws of composition
51A05 General theory of linear incidence geometry and projective geometries
06A06 Partial orders, general

Citations:

Zbl 0693.06003
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References:

[1] Lenz H.: Vorlesungen über projektive Geometrie. Leipzig, 1965, S. 360. · Zbl 0134.16203
[2] Machala F.: Konstruktionen einiger endlicher modularer Inzidenzstrukturen. Acta Univ. Palacki. Olomuc., Fac. rer. nat. 100 (1991), 235-253. · Zbl 0764.51011
[3] Rachůnek J., Larmerová J.: Translation of distributive and modular sets. Acta Univ. Palacki. Olomuc., Fac. rer. nat. 91 (1988), 13-25. · Zbl 0693.06003
[4] Wille R.: Restructuring lattice theory: an approach based on hierarchies of concepts. I. Rival (ed.). Ordered sets. Riedel, Dordrecht-Boston, 1982, 445-470. · Zbl 0491.06008
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