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Abelian GroupsDivisibility and Injectivity

Abelian Groups: Divisibility and Injectivity [Most perfect objects in the category of abelian groups are those groups in which we can also ‘divide:’ for every element a and for every positive integer n, the equation nx = a has a (not necessarily unique) solution for x in the group. These objects are the divisible groups which are universal in the sense that every group can be embedded as a subgroup in a suitable divisible group.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Abelian GroupsDivisibility and Injectivity

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

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Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2015
ISBN
978-3-319-19421-9
Pages
131 –148
DOI
10.1007/978-3-319-19422-6_4
Publisher site
See Chapter on Publisher Site

Abstract

[Most perfect objects in the category of abelian groups are those groups in which we can also ‘divide:’ for every element a and for every positive integer n, the equation nx = a has a (not necessarily unique) solution for x in the group. These objects are the divisible groups which are universal in the sense that every group can be embedded as a subgroup in a suitable divisible group.]

Published: Jun 12, 2015

Keywords: Abelian Group; Left Ideal; Injective Group; Torsion Group; Divisible Group

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