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Title: Poor and pi-poor Abelian groups
Authors: Alizade, Rafail
Büyükaşık, Engin
Büyükaşık, Engin
Izmir Institute of Technology. Mathematics
Keywords: Injective modules
Poor abelian groups
Issue Date: Jan-2017
Publisher: Taylor and Francis Ltd.
Source: Alizade, R., and Büyükaşık, E. (2017). Poor and pi-poor Abelian groups. Communications in Algebra, 45(1), 420-427. doi:10.1080/00927872.2016.1175585
Abstract: In this paper, poor abelian groups are characterized. It is proved that an abelian group is poor if and only if its torsion part contains a direct summand isomorphic to (Formula presented.) , where P is the set of prime integers. We also prove that pi-poor abelian groups exist. Namely, it is proved that the direct sum of U(ℕ), where U ranges over all nonisomorphic uniform abelian groups, is pi-poor. Moreover, for a pi-poor abelian group M, it is shown that M can not be torsion, and each p-primary component of M is unbounded. Finally, we show that there are pi-poor groups which are not poor, and vise versa.
ISSN: 0092-7872
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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