Annihilator equivalence of torsion-free abelian groups
1992 ◽
Vol 52
(1)
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pp. 119-129
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AbstractWe define an equivalence relation on the class of torsion-free abelian groups under which two groups are equivalent ifevery 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.
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2018 ◽
Vol 167
(02)
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pp. 229-247
Keyword(s):
2006 ◽
Vol 06
(02)
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pp. 233-251
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Keyword(s):
2011 ◽
Vol 43
(6)
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pp. 1198-1204
2007 ◽
Vol 35
(3)
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pp. 1055-1072
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1985 ◽
Vol 93
(2)
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pp. 227-227
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