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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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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