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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0251072-X
MathSciNet review:
0251072
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Abstract | References | Similar Articles | Additional Information
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
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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