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On the finiteness problem for classes of modular lattices

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Abstract

The finiteness problem is shown to be unsolvable for any sufficiently large class of modular lattices.

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References

  1. Adyan, I.: Algorithmic unsolvability of problems of recognition of certain properties of groups. Dokl. Akad. Nauk SSSR (N.S.) 103, 533–535 (1955) (Russian)

  2. Adyan, S.I.: Unsolvability of some algorithmic problems in the theory of groups. Trudy Moskov. Math. Obsc. 6, 231–298 (1957) (Russian)

  3. Day, A., Herrmann, C., Wille, R.: On modular lattices with four generators. Algebra Univ. 2, 317–323 (1972)

    Article  MathSciNet  Google Scholar 

  4. Herrmann, C., Tsukamoto, Y., Ziegler, M.: On the consistency problem for modular lattices and related structures. Int. J. Algebra Comput. 26, 1573–1595 (2016)

    Article  MathSciNet  Google Scholar 

  5. Rabin, M.O.: Recursive unsolvability of group theoretic problems. Ann. Math. 67, 172–194 (1958)

    Article  MathSciNet  Google Scholar 

  6. Slavik, V.: Finiteness of finitely presented lattices. In: Lattice theory and its applications (Darmstadt, 1991). Res. Exp. Math. 23, 219–227. Heldermann, Lemgo (1995)

  7. Wille, R.: Über modulare Verbände, die von einer endlichen halbgeordneten Menge frei erzeugt werden. Math. Z. 131, 241–249 (1973) (German)

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Correspondence to Christian Herrmann.

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Dedicated to the memory of Rudolf Wille.

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Herrmann, C. On the finiteness problem for classes of modular lattices. Algebra Univers. 80, 4 (2019). https://doi.org/10.1007/s00012-019-0579-3

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