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Parallelism in Symmetric Lattices

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Book cover Theory of Symmetric Lattices

Part of the book series: Die Grundlehren der mathematischen Wissenschaften ((GL,volume 173))

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Abstract

In this chapter we use the term “point” instead of “atom”, for the arguments here are geometric. Moreover, an element a of an AC-lattice is called a line (resp. a plane) when h(a)=2 (resp. h(a)=3), as in a matroid lattice.

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References for Chspter IV

  1. Dubreil-Jacotin, M. L., L. Leisieur and R. Croisot, Leçons sur la théorie des treillis des structures algébriques ordonnées et des treillis géométriques. Paris: Gauthier-Villars 1953.

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  2. Hsu, C.-J. On lattice theoretic characterization of the parallelism in affine geometry. Ann. of Math. 50, 188–203 (1949).

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  3. Maeda, F. Modular centers of affine matroid lattices. J. Sci. Hiroshima Univ., Ser. A-I27, 73–84 (1963).

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  4. Maeda, F. Parallel mappings and comparability theorems in affine matroid lattices. J. Sci. Hiroshima Univ., Ser. A-I27, 85–96 (1963).

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  5. Maeda, F. Point-free parallelism in Wilcox lattices. J. Sci. Hiroshima Univ., Ser. A-I28, 10–32 (1964).

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  6. Sasaki, U. Lattice theoretic characterization of an affine geometry of arbitrary dimensions. J. Sci. Hiroshima Univ., Ser. A 16, 223–238 (1953).

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  7. Sasaki, U. Lattice theoretic characterization of geometries satisfying “Axiome der Verknüpfung”. J. Sci. Hiroshima Univ., Ser. A 16, 417–423 (1953).

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Authors and Affiliations

  1. Hiroshima University, Japan

    Prof. Dr. Fumitomo Maeda (Late Professor of Mathematics)

  2. Ehime University, Japan

    Prof. Dr. Shûichirô Maeda (Professor of Mathematics)

Authors
  1. Prof. Dr. Fumitomo Maeda
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  2. Prof. Dr. Shûichirô Maeda
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© 1970 Springer-Verlag Berlin · Heidelberg

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Maeda, F., Maeda, S. (1970). Parallelism in Symmetric Lattices. In: Theory of Symmetric Lattices. Die Grundlehren der mathematischen Wissenschaften, vol 173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46248-1_4

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  • DOI: https://doi.org/10.1007/978-3-642-46248-1_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-46250-4

  • Online ISBN: 978-3-642-46248-1

  • eBook Packages: Springer Book Archive

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