Hereditarily pure associative algebras over a Dedekind ring whose maximal ideals have finite indices

Hereditarily pure associative algebras over a Dedekind ring whose maximal ideals have finite indices

It is proved that an algebra over a Dedekind ring whose maximal ideals have finite indices is hereditarily pure iff it is representable as a direct sum of an elementary Abelian algebra and an elementary Jacobsonian algebra.

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Veröffentlicht in:Algebra and logic 2012, Vol.50 (6), p.526-538
1. Verfasser: Martynov, L. M.
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Algebra
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
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creator Martynov, L. M.
description It is proved that an algebra over a Dedekind ring whose maximal ideals have finite indices is hereditarily pure iff it is representable as a direct sum of an elementary Abelian algebra and an elementary Jacobsonian algebra.
doi_str_mv 10.1007/s10469-012-9163-z
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subjects Algebra
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
title Hereditarily pure associative algebras over a Dedekind ring whose maximal ideals have finite indices
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