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.
- H. Jacobinski, Genera and decompositions of lattices over orders, Acta Math. 121 (1968), 1–29. MR 251063, DOI https://doi.org/10.1007/BF02391907
- A. V. Roĭter, Integer-valued representations belonging to one genus, Izv. Akad. Nauk SSSR Ser. Mat. 30 (1966), 1315–1324 (Russian). MR 0213391
H. Jacobinski, Genera and decompositions of lattices over orders, Acta. Math. 121 (1968), 1-29.
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.
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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