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MODULES WITH ABELIAN ENDOMORPHISM RINGS

Part of: Modules, bimodules and ideals

Published online by Cambridge University Press:  18 June 2010

GRIGORE CĂLUGĂREANU  and
PHILL SCHULTZ
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: calu@math.ubbcluj.ro)
PHILL SCHULTZ*
Affiliation:
School of Mathematics and Statistics, University of Western Australia, Nedlands, WA 6009, Australia (email: schultz@maths.uwa.edu.au)
*
✉For correspondence; e-mail: schultz@maths.uwa.edu.au
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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.

Keywords

commutative endomorphism ringscentral or commuting idempotentsduo ringsunique complementsfully invariant submodules

MSC classification

Secondary: 16D70: Structure and classification (except as in ), direct sum decomposition, cancellation
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 1 , August 2010 , pp. 99 - 112
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

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