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Abelian GroupsDirect Sums and Direct Products

Abelian Groups: Direct Sums and Direct Products [The concept of direct sum is of utmost importance for the theory. This is mostly due to two facts: first, if we succeed in decomposing a group into a direct sum, then it can be studied by investigating the summands separately, which are, in numerous cases, simpler to deal with. We shall see that almost all structure theorems in abelian group theory involve, explicitly or implicitly, some direct decomposition. Secondly, new groups can be constructed as direct sums of known or previously constructed groups.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Abelian GroupsDirect Sums and Direct Products

Part of the Springer Monographs in Mathematics Book Series
Fuchs, László
Abelian Groups — Jun 12, 2015
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31 pages

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Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2015
ISBN
978-3-319-19421-9
Pages
43 –74
DOI
10.1007/978-3-319-19422-6_2
Publisher site
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Abstract

[The concept of direct sum is of utmost importance for the theory. This is mostly due to two facts: first, if we succeed in decomposing a group into a direct sum, then it can be studied by investigating the summands separately, which are, in numerous cases, simpler to deal with. We shall see that almost all structure theorems in abelian group theory involve, explicitly or implicitly, some direct decomposition. Secondly, new groups can be constructed as direct sums of known or previously constructed groups.]

Published: Jun 12, 2015

Keywords: Exact Sequence; Direct Product; Inverse Limit; Subdirect Product; Direct Decomposition

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