J Austral Math Soc Ser A 52 pp119--129, 1992.

Annihilator Equivalence of Torsion-Free Abelian Groups

P. Schultz, C. Vinsonhaler and W. J. Wickless

Abstract

We define an equivalence relation on the class of torsion-free abelian groups under which two groups are equivalent if every pure subgroup of one has a non-zero image in the other, and each has a non-zero image in every torsion-free factor of the other. We study the closure properties of the equivalence classes, and the structural properties of the class of all equivalence classes. Finally we identify a class of groups which satisfy Krull-Schmidt and Jordan-Hölder properties with respect to the equivalence.

1991 AMS Subject Classification: 20K15

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Authors

P. Schultz

University of Western Australia, Nedlands, Western Australia, 6009, Australia.

C. Vinsonhaler

University of Connecticut, Storrs, Connecticut, 06268, U.S.A.

W. J. Wickless

University of Connecticut, Storrs, Connecticut, 06268, U.S.A.