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2010•Bulletin of the Australian Mathematical SocietyOpen access

MODULES WITH ABELIAN ENDOMORPHISM RINGS

Grigore Călugăreanu, Phill Schultz

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Abstract

Abstract 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.

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Abstract 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.

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Available abstract

Abstract 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.

Key concepts: Endomorphism, Mathematics, Abelian group, Pure mathematics, Commutative property, Invariant (physics), Endomorphism ring, Rank of an abelian group

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