Homogeneously Decomposable Modules

George Kolettis
Additional contact information
George Kolettis: University of Notre Dame

Chapter [13] in Études sur les Groupes abéliens / Studies on Abelian Groups, 1968, pp 223-238 from Springer

Abstract: Abstract The well known theorem of Baer-Kulikov-Kaplansky asserts that a direct summand of a completely decomposable torsion-free abeliah group is again completely decomposable. The study of completely decomposable torsion-free abelian groups was initiated by Baer in [1]. One of the results he proved is that direct summands of such a group are completely decomposable whenever the group satisfies a maximum condition. Kulikov [8] proved that every countable direct summand of an arbitrary completely decomposable torsion-free abelian group is completely decomposable, a nontrivial result. By proving that a direct summand of a direct sum of countably generated modules is again a direct sum of countably generated modules, Kaplan sky [7] obtained the complete theorem. An important contribution was also made by Fuchs [5], vko gave an elegant and much shorter proof of Kulikov’s result.

Keywords: Prime Ideal; Nonzero Element; Direct Summand; Height Function; Nonzero Ideal (search for similar items in EconPapers)
Date: 1968
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-46146-0_13

Ordering information: This item can be ordered from
http://www.springer.com/9783642461460

DOI: 10.1007/978-3-642-46146-0_13

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().