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A class of pure subgroups of completely decomposable abelian groups
Author:
David M. Arnold
Journal:
Proc. Amer. Math. Soc. 41 (1973), 37-44
MSC:
Primary 20K25
MathSciNet review:
0325806
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Abstract: Direct sum decompositions of the class of pure subgroups of finite rank completely decomposable torsion free abelian groups with typesets of cardinality at most 4 are considered. In certain cases, the indecomposable groups are classified, resulting in new proofs of several theorems by T. B. Cruddis.
- [1]
D. Arnold and E. L. Lady, Endomorphism rings and direct sums of torsion free Abelian groups (to appear).
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M.
C. R. Butler, A class of torsion-free abelian groups of finite
rank, Proc. London Math. Soc. (3) 15 (1965),
680–698. MR 0218446
(36 #1532)
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T.
B. Cruddis, On a class of torsion-free abelian groups, Proc.
London Math. Soc. (3) 21 (1970), 243–276. MR 0271221
(42 #6104)
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L.
Fuchs, Abelian groups, International Series of Monographs on
Pure and Applied Mathematics, Pergamon Press, New York, 1960. MR 0111783
(22 #2644)
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László
Fuchs, Infinite abelian groups. Vol. I, Pure and Applied
Mathematics, Vol. 36, Academic Press, New York, 1970. MR 0255673
(41 #333)
- [1]
- D. Arnold and E. L. Lady, Endomorphism rings and direct sums of torsion free Abelian groups (to appear).
- [2]
- M. C. R. Butler, A class of torsion-free Abelian groups of finite rank, Proc. London Math. Soc. (3) 15 (1965), 680-698. MR 36 #1532. MR 0218446 (36:1532)
- [3]
- T. B. Cruddis, On a class of torsion-free Abelian groups, Proc. London Math. Soc. (3) 21 (1970), 243-276. MR 42 #6104. MR 0271221 (42:6104)
- [4]
- L. Fuchs, Abelian groups, Akad. Kiadó, Budapest, 1958; republished by Internat. Series of Monos on Pure and Appl. Math., Pergamon Press, New York, 1960. MR 21 #5672; 22 #2644. MR 0111783 (22:2644)
- [5]
- -, Infinite Abelian groups. Vol. I, Pure and Appl. Math., vol. 36, Academic Press, New York, 1970. MR 41 #333. MR 0255673 (41:333)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1973-0325806-2
PII:
S 0002-9939(1973)0325806-2
Keywords:
Torsion free abelian groups of finite rank,
completely decomposable groups
Article copyright:
© Copyright 1973 American Mathematical Society
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