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Stable modular lattices of small height. (English. Russian original) Zbl 0881.06001

Sib. Math. J. 37, No. 3, 618-625 (1996); translation from Sib. Mat. Zh. 37, No. 3, 704-713 (1996).
Modular lattices of dimension (=height=length) \(n\leq 4\) are well understood [cf. B. Jónsson, Math. Scand. 7, 133-145 (1959; Zbl 0095.34602)]. From this the author derives that the ones not containing a projective plane as an (interval) sublattice are stable in the model-theoretic sense. His notion of ‘height’ is ‘dimension’ \(+1\).

MSC:

06C05 Modular lattices, Desarguesian lattices
03C45 Classification theory, stability, and related concepts in model theory

Citations:

Zbl 0095.34602
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References:

[1] K. A. Meirembekov and K. M. Shegirov, ”Stable geometric lattices,” Sibirsk. Mat. Zh.,34, No. 3, 122–131 (1993). · Zbl 0860.03030
[2] A. Day, ”Geometrical applications in modular lattices,” in: Lecture Notes in Math., Springer, Berlin, 1983,1004, pp. 111–141.
[3] G. Birkhoff, Lattice Theory [Russian translation], Nauka, Moscow (1984).
[4] A. I. Shirshov and A. A. Nikitin, Algebraic Theory of Projective Planes [in Russian], Novosibirsk. Univ., Novosibirsk (1987). · Zbl 0692.51001
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