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Abelian GroupsPurity and Basic Subgroups

Abelian Groups: Purity and Basic Subgroups [In this chapter, we are going to discuss a basic concept: pure subgroup. This concept has been one of the most fertile notions in the theory since its inception in a paper by the pioneer H. Prüfer. The relevance of purity in abelian group theory, and later in module theory, has tremendously grown with time. While abelian groups have been major motivation for a number of theorems in category theory, purity has served as a prototype for relative homological algebra, and has played a significant role in model theory as well.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Abelian GroupsPurity and Basic Subgroups

Part of the Springer Monographs in Mathematics Book Series
Fuchs, László
Springer Journals — Jun 12, 2015
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33 pages

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Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2015
ISBN
978-3-319-19421-9
Pages
149 –181
DOI
10.1007/978-3-319-19422-6_5
Publisher site
See Chapter on Publisher Site

Abstract

[In this chapter, we are going to discuss a basic concept: pure subgroup. This concept has been one of the most fertile notions in the theory since its inception in a paper by the pioneer H. Prüfer. The relevance of purity in abelian group theory, and later in module theory, has tremendously grown with time. While abelian groups have been major motivation for a number of theorems in category theory, purity has served as a prototype for relative homological algebra, and has played a significant role in model theory as well.]

Published: Jun 12, 2015

Keywords: Injective Property; Pure Subgroup; Basic Subgroup; Infinite Cyclic Group; Splitting Exact Sequence

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