• Martin Aigner
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 234)


After having introduced in chapter I the main classes of mappings, let us now study in some depth the various types of lattices encountered there. It seems appropriate to proceed from the most special class of distributive lattices to the more general types, modular, semimodular, and geometric lattices, particularly in view of the fact that each of the three characterizations we shall derive for distributive lattices will lead directly to an important branch of combinatorial theory: matroids and combinatorial geometries to be discussed in chapters VI and VII, the inversion calculus (chapters III and IV), and transversal theory (chapter VIII).


Distributive Lattice Rank Function Division Ring Modular Lattice Irreducible Element 
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Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Martin Aigner
    • 1
  1. 1.II. Institut für MathematikFreie Universität BerlinBerlin 33Federal Republic of Germany

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