Faithful abelian groups of infinite rank

Author:
Ulrich Albrecht

Journal:
Proc. Amer. Math. Soc. **103** (1988), 21-26

MSC:
Primary 20K20; Secondary 20K30

DOI:
https://doi.org/10.1090/S0002-9939-1988-0938637-8

MathSciNet review:
938637

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a subgroup of an abelian group such that is isomorphic to a direct sum of copies of an abelian group . For to be a direct summand of , it is necessary that be generated by and all homomorphic images of in . However, if the functor preserves direct sums of copies of , then this condition is sufficient too if and only if is nonzero for all nonzero right -modules . Several examples and related results are given.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0938637-8

Keywords:
Endomorphism ring,
faithful,
Baer's lemma

Article copyright:
© Copyright 1988
American Mathematical Society