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On embedding of lattices belonging to the same genus

Author: H. Jacobinski
Journal: Proc. Amer. Math. Soc. 24 (1970), 134-136
MSC: Primary 16.50
MathSciNet review: 0251072
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Abstract: If $ R$ is an order in a semisimple algebra over a Dedekind ring and $ M,\;N$ two $ R$-lattices in the same genus, an upper bound for the length of the composition series of $ M/N'$ for $ N' \cong N$, is given. This answers a question posed by Roĭter.

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  • [1] H. Jacobinski, Genera and decompositions of lattices over orders, Acta. Math. 121 (1968), 1-29. MR 0251063 (40:4294)
  • [2] A. V. Roĭter, Integer-valued representations belonging to one genus, Izv. Akad. Nauk SSSR Sen Mat. 30 (1966), 1315-1324; English transl., Amer. Math. Soc. Transl. (2) 71 (1968), 49-59. MR 35 #4255. MR 0213391 (35:4255)

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Keywords: Representation of orders over a Dedekind ring, genus of representation modules, isomorphism classes in a genus, Dirichlet's theorem on arithmetic progressions
Article copyright: © Copyright 1970 American Mathematical Society

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