Abstract
We investigate full subcategories of the category Ab of Abelian groups that are simultaneously reflective and coreflective in Ab. Such subcategories are exactly those isomorphic to categories of modules that are fully embedded into Ab. Rings giving rise to such modules are completely described. One of the curious special cases is provided by the full subcategory of Ab consisting of all torsion-free, divisible Abelian groups, which can be characterized, alternatively as the reflective hull of ℚ in Ab, or as the coreflective hull of ℚ in Ab, or as the intersection of the epireflective hull of ℚ in Ab with the monocoreflective hull of ℚ in Ab.
To our friends, Lamar Bentley and George Strecker, on the occasion of their 60th birthday — with affection and gratitude
The author acknowledges the support of the Czech Republic grant 201/98/P247 and MSM 113200007.
The author acknowledges the support of the Czech Republic grant 201/00/1466 and MSM 113200007.
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El Bashir, R., Herrlich, H., Hušek, M. (2001). Abelian Groups: Simultaneously Reflective and Coreflective Subcategories versus Modules. In: Koslowski, J., Melton, A. (eds) Categorical Perspectives. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1370-3_15
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DOI: https://doi.org/10.1007/978-1-4612-1370-3_15
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7117-8
Online ISBN: 978-1-4612-1370-3
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