Abstract
For modular lattices of finite length, vector space representations are shown to give rise to contracted representations of homomorphic images
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References
D. J.Benson and J. H.Conway (1985) Diagrams for modular lattices, J. Pure and Applied Algebra 37, 111–116.
P.Crawley and R. P.Dilworth (1973) Algebraic Theory of Lattices Prentice Hall Englewood Cliffs.
G.Czédli and G.Hutchinson (1987) An irregular Horn sentence in submodule lattices, Acta Sci. Math. 51, 35–38.
A.Day, C.Herrmann, and R.Wille (1972) On modular lattices with four generators, Algebra Universalis 2, 317–323.
B.Ganter, W.Poguntke, and R.Wille (1981) Finite substances of four-generated modular lattices, Algebra Universalis 12, 160–171.
I. M.Gel'fand and V. A.Ponomarev (1977) Lattices, representations, and algebras connected with them, Russian Math. Surveys 31, 67–85.
C.Herrmann and M.Wild (1991) Acyclic modular lattices and their representations, J. Algebra 136, 17–36.
C. Herrmann, D. Pickering, and M. Roddy, Geometric descriptions of modular lattices, to appear in Algebra Universalis.
J. B. Nation, Jónsson's contributions to lattice theory, to appear in Algebra Universalis.
W.Poguntke (1975) Zerlegung von S-Verbänden, Math. Z. 142, 47–65.
M. Wild, Cover preserving embedding of modular lattices into partition lattices, to appear in Discrete Mathematics.
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Communicated by B. Jónsson
Dedicated to the memory of Alan Day
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Herrmann, C. On the contraction of vectorial lattice representations. Order 8, 275–281 (1991). https://doi.org/10.1007/BF00383448
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DOI: https://doi.org/10.1007/BF00383448