Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Affine geometry: a lattice characterization

Author: M. K. Bennett
Journal: Proc. Amer. Math. Soc. 88 (1983), 21-26
MSC: Primary 51D25; Secondary 05B35, 06C10
MathSciNet review: 691271
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Necessary and sufficient conditions are given for a lattice $ L$ to be the lattice of flats of an affine space of arbitrary (possibly infinite) dimension.

References [Enhancements On Off] (What's this?)

  • [A1] E. Artin, Geometric algebra, Interscience, New York, 1957. MR 0082463 (18:553e)
  • [B1] G. Birkhoff, Lattice theory (third ed.), Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R. I., 1967. MR 0227053 (37:2638)
  • [B2] -, Combinatorial relations in projective geometry, Ann. of Math. (2) 36 (1935), 743-748. MR 1503250
  • [G1] S. Gorn, On incidence geometry, Bull. Amer. Math. Soc. 46 (1940), 158-167. MR 0001006 (1:165d)
  • [H1] D. Hilbert, Foundations of geometry (transl. by E. J. Townsend), Open Court, LaSalle, Ill., 1902. (Reprinted, 1950) MR 0275262 (43:1019)
  • [M1] F. Maeda and S. Maeda, Theory of symmetric lattices, Springer, New York, 1970. MR 0282889 (44:123)
  • [M2] K. Menger, New foundations of projective and affine geometry, Ann. of Math. (2) 37 (1936), 456-482. MR 1503293
  • [S1] U. Sasaki, Lattice theoretic characterization of geometries satisfying "Axiome der Verknüpfung", Hiroshima Math. J. Ser. A 16 (1953), 417-423. MR 0060837 (15:736a)
  • [S2] -, Lattice theoretic characterization of affine geometry of arbitrary dimension, Hiroshima Math. J. Ser. A 16 (1952), 223-238. MR 0060473 (15:674b)
  • [S3] E. Snapper and R. Troyer, Metric affine geometry, Academic Press, New York, 1971. MR 0300190 (45:9238)
  • [W1] O. Wyler, Incidence geometry, Duke Math. J. 20 (1953), 601-610. MR 0058227 (15:340b)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 51D25, 05B35, 06C10

Retrieve articles in all journals with MSC: 51D25, 05B35, 06C10

Additional Information

Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society