A note on the existence of torsion-free modules with a prescribed type-set

De Munter-Kuyl, Lucie

doi:10.1090/S0002-9939-1980-0581020-0

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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A note on the existence of torsion-free modules with a prescribed type-set
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by Lucie De Munter-Kuyl PDF

Proc. Amer. Math. Soc. 80 (1980), 531-532 Request permission

Abstract:

In [2], Ito has proved the existence of a completely anisotropic torsion-free abelian group of rank two with a prescribed type-set. We outline here an alternative construction in a more general setting.

References

Lucie De Munter-Kuyl, Isomorphisms of rank two torsion-free modules over a Dedekind domain, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 60 (1976), no. 4, 351–358 (English, with Italian summary). MR 469911
Ryuichi Ito, On type sets of torsion-free abelian groups of rank $2$, Proc. Amer. Math. Soc. 48 (1975), 39–42. MR 354900, DOI 10.1090/S0002-9939-1975-0354900-7