On torsion-free abelian 𝑘-groups

Dugas, Manfred; Rangaswamy, K. M.

doi:10.1090/S0002-9939-1987-0875371-6

On torsion-free abelian $k$-groups
HTML articles powered by AMS MathViewer

by Manfred Dugas and K. M. Rangaswamy PDF

Proc. Amer. Math. Soc. 99 (1987), 403-408 Request permission

Abstract:

It is shown that a knice subgroup with cardinality ${\aleph _1}$, of a torsion-free completely decomposable abelian group, is again completely decomposable. Any torsion-free abelian $k$-group of cardinality ${\aleph _n}$ has balanced projective dimension $\leq n$.

References

Maurice Auslander, On the dimension of modules and algebras. III. Global dimension, Nagoya Math. J. 9 (1955), 67–77. MR 74406, DOI 10.1017/S0027763000023291
Paul C. Eklof, Set-theoretic methods in homological algebra and abelian groups, Séminaire de Mathématiques Supérieures [Seminar on Higher Mathematics], vol. 69, Presses de l’Université de Montréal, Montreal, Que., 1980. MR 565449
László Fuchs, Infinite abelian groups. Vol. II, Pure and Applied Mathematics. Vol. 36-II, Academic Press, New York-London, 1973. MR 0349869
Paul Hill, Isotype subgroups of totally projective groups, Abelian group theory (Oberwolfach, 1981) Lecture Notes in Math., vol. 874, Springer, Berlin-New York, 1981, pp. 305–321. MR 645937
Paul Hill and Charles Megibben, Axiom $3$ modules, Trans. Amer. Math. Soc. 295 (1986), no. 2, 715–734. MR 833705, DOI 10.1090/S0002-9947-1986-0833705-6
Paul Hill and Charles Megibben, Torsion free groups, Trans. Amer. Math. Soc. 295 (1986), no. 2, 735–751. MR 833706, DOI 10.1090/S0002-9947-1986-0833706-8