On the lattice of right ideals of the endomorphism ring of an abelian group

DOI10.1017/S0004972700027556zbMath0644.20033MaRDI QIDQ3786644

Theodore G. Faticoni

Publication date: 1988

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

subgroups of finite indexcategory equivalenceendomorphism ringtorsion-free abelian groupsfinitely generated End A modules

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Module categories in associative algebras (16D90) Homological and categorical methods for abelian groups (20K40) Torsion-free groups, finite rank (20K15) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (5)

A new proof of the baer-kaplansky theorem ⋮ Gabriel filters on the endomorphism ring of a torsion-free abelian group ⋮ Centrally essential torsion-free rings of finite rank ⋮ Centrally essential endomorphism rings of abelian groups ⋮ Abelian groups flat as modules over their endomorphism ring

Cites Work

• Semi-local localizations of rings and subdirect decompositions of modules
• Finite rank torsion free Abelian groups and rings
• Nearly isomorphic torsion free abelian groups
• Abelian groups, \(A\), such that \(\Hom(A,-)\) preserves direct sums of copies of \(A\)
• Rings whose faithful modules are flat over their endomorphism rings
• Primary abelian groups as modules over their endomorphism rings
• Baer's Lemma and Fuchs' Problem 84a
• Endomorphism Rings and Direct Sums of Torsion Free Abelian Groups
• On subcommutative rings

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