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MODULES WITH ABELIAN ENDOMORPHISM RINGS

Published online by Cambridge University Press:  18 June 2010

GRIGORE CĂLUGĂREANU
Affiliation:
Babeş-Bolyai University Cluj-Napoca, Faculty of Mathematics and Computer Science, Str. Mihail Kogălniceanu nr. 1, RO-400084 Cluj-Napoca, Romania (email: [email protected])
PHILL SCHULTZ*
Affiliation:
School of Mathematics and Statistics, University of Western Australia, Nedlands, WA 6009, Australia (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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The results of Szele and Szendrei [‘On Abelian groups with commutative endomorphism rings’, Acta Math. Acad. Sci. Hungar.2 (1951), 309–324] characterizing abelian groups with commutative endomorphism rings are generalized to modules whose endomorphism rings have various restrictions on their idempotents. Such properties include central or commuting idempotents, and one-sided ideals being two-sided. Related properties include direct summands having unique complements, or being fully invariant.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

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