Abstract
In the initial development of lattice theory considerable attention was devoted to the structure of modular lattices. Two of the principal structure theorems which came out of this early work are the following:
Every complemented modular lattice of finite dimensions is a direct union of a finite number of simple1 complemented modular lattices (Birkhoff [1], Menger [4]).
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References
G. Birkhoff. Combinational relations in projective geometries. Ann. of Math. 36(1935), 743–748.
G. Birkhoff. Lattice Theory, Revised edition, Amer. Math. Soc. Colloquium Publications, Vol. 25, 1948.
G. Birkhoff. Subdirect unions in universal algebra. Bull. Amer. Math. Soc. 50 (1944), 764–768.
K. Menger. New foundations of projective and affine geometry. Ann. of Math. 37 (1936), 456–482.
N. Funayama and T. Nakayama. On the distributivity of a lattice of lattice-congruences Proc. Imp. Acad. Tokyo 18 (1942), 553–554.
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Dilworth, R.P. (1990). The Structure of Relatively Complemented Lattices. In: Bogart, K.P., Freese, R., Kung, J.P.S. (eds) The Dilworth Theorems. Contemporary Mathematicians. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-3558-8_39
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DOI: https://doi.org/10.1007/978-1-4899-3558-8_39
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