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Group-valued charges: common extensions and the infinite Chinese remainder property


Authors: K. P. S. Bhaskara Rao and R. M. Shortt
Journal: Proc. Amer. Math. Soc. 113 (1991), 965-972
MSC: Primary 28B10; Secondary 20K99
DOI: https://doi.org/10.1090/S0002-9939-1991-1059633-9
MathSciNet review: 1059633
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Abstract: We exhibit two consistent, integer-valued charges (finitely additive measures) which do not have a common, integer-valued extension. More generally, after introducing the notion of an infinitary Chinese remainder property for Abelian groups, we show that if a group has the common extension property, then the group must have the infinite Chinese remainder property. The class of groups with the common extension property is characterised as coincident with the class of cotorsion groups.


References [Enhancements On Off] (What's this?)

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  • [2] K. P. S. Bhaskara Rao and R. M. Shortt, Common extensions for homomorphisms and groups-valued charges, Rend. Circ Mat. (Palermo) (to appear).
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1059633-9
Keywords: Charge, Chinese remainder theorem, cotorsion group, algebraically compact group
Article copyright: © Copyright 1991 American Mathematical Society

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