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Proceedings of the American Mathematical Society

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

 

 

On splitting augmentation ideals


Author: Warren Dicks
Journal: Proc. Amer. Math. Soc. 83 (1981), 221-227
MSC: Primary 16A27
DOI: https://doi.org/10.1090/S0002-9939-1981-0624902-4
MathSciNet review: 624902
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Abstract: Let $ G$ be a group, $ H$ a subgroup of $ G$ and $ R$ an associative ring. Write $ \omega (RG)$ for the augmentation ideal of the group ring $ RG$, and $ \omega (RH)G$ for the right ideal of $ RG$ generated by $ \omega (RH)$. For $ G$ finitely generated over $ H$ we characterize, in terms of the Bass-Serre theory of groups acting on trees, the situation where $ \omega (RH)G$ is an $ RG$-summand of $ \omega (RG)$.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0624902-4
Keywords: Group ring, augmentation ideal of a subgroup, groups acting on trees, fundamental group of a graph of groups, derivation
Article copyright: © Copyright 1981 American Mathematical Society