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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Fundamental groups of topological $ R$-modules


Author: Ann Bateson
Journal: Trans. Amer. Math. Soc. 270 (1982), 525-536
MSC: Primary 57T20; Secondary 08B99
DOI: https://doi.org/10.1090/S0002-9947-1982-0645328-9
MathSciNet review: 645328
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Abstract: The main result of this paper is that if $ R$ is a countable, Noetherian ring, then the underlying abelian group of every $ R$-module is isomorphic to the fundamental group of some topological $ R$-module. As a corollary, it is shown that for certain varieties $ V$(e.g., varieties of finite type) every abelian group in $ V$ is isomorphic to the fundamental group of some arcwise connected topological algebra in $ V$.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0645328-9
Article copyright: © Copyright 1982 American Mathematical Society

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