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Layer-Projective Lattices. II

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The main result of this paper is: any primary Arguesian lattice over the field GF(p) of geometric dimension at least three is isomorphic to the lattice of all submodules of a finitely generated module over the ring of polynomials of bounded degree over the field GF(p).

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REFERENCES

  1. M. Suzuki, Structure of a Group and the Structure of Its Lattice of Subgroups, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1956.

    Google Scholar 

  2. B. V. Yakovlev, “Conditions under which a lattice is isomorphic to the lattice of subgroups of a group,” Algebra i Logika [Algebra and Logic], 13 (1974), no. 6, 694–712.

    Google Scholar 

  3. S. A. Anishchenko, “On the representation of some modular lattices by lattices of subgroups,” Matem. Zapiski Krasnoyarsk. Gospedinst. (1965), no. 1, 1–21.

    Google Scholar 

  4. V. A. Antonov and Yu. A. Nazyrova, “Layer-projective lattices. I,” Mat. Zametki [Math. Notes], 63 (1998), no. 2, 170–182.

    Google Scholar 

  5. B. Jonsson and G. Monk, “Representations of primary arguesian lattices,” Pacific J. Math., 30 (1969), no. 1, 95–139.

    Google Scholar 

  6. G. S. Monk, “Desargues' law and the representation of primary lattices,” Pacific J. Math., 30 (1969), no. 1, 175–186.

    Google Scholar 

  7. V. A. Antonov, “On a class of modular lattices of finite length,” Algebra i Logika [Algebra and Logic], 30 (1991), no. 1, 3–14.

    Google Scholar 

  8. B. Jonsson, “Modular lattices and Desargues theorem,” Math. Scand., 2 (1953), 205–314.

    Google Scholar 

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Antonov, V.A., Nazyrova, Y.A. Layer-Projective Lattices. II. Mathematical Notes 72, 145–151 (2002). https://doi.org/10.1023/A:1019885508998

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  • DOI: https://doi.org/10.1023/A:1019885508998

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