Endomorphism Rings and Direct Sums of Torsion Free Abelian Groups

DOI10.2307/1997231zbMath0329.20033OpenAlexW4247100544MaRDI QIDQ4095070

No author found.

Publication date: 1975

Full work available at URL: https://doi.org/10.2307/1997231

Mathematics Subject Classification ID

Direct sums, direct products, etc. for abelian groups (20K25) Abelian groups (20Kxx) Torsion-free groups, finite rank (20K15)

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Pure subgroups of \(A\)-projective groups, Coefficient rings of multidimensional torus extensions, Block rigid almost completely decomposable groups and lattices over multiple pullback rings, Semi-local localizations of rings and subdirect decompositions of modules, Abelian groups with semi-simple Artinian quasi-endomorphism rings, The integral closure of \({\mathbb{Z}}\) in the Grothendieck ring for quasi- isomorphism classes of finite rank torsion free modules over a Dedekind domain, Strongly D2 modules and their applications, A class of Abelian groups with hereditary rings of endomorphisms, DIAGRAMS OF AN ABELIAN GROUP, Torsion-free Abelian groups torsion over their endomorphism rings, Influence of the Baer-Kaplansky theorem on the development of the theory of groups, rings, and modules, Abelian groups with self-injective quasi-endomorphism rings., On the lattice of right ideals of the endomorphism ring of an abelian group, Endomorphism rings of faithfully flat Abelian groups, Separative cancellation and multiple isomorphism in torsion-free Abelian groups, Tight subgroups in almost completely decomposable groups, Properties of Abelian Groups Determined by Their Endomorphism Ring, On the quasi-splitting of exact sequences, Endomorphism rings of modules and lattices of submodules, Faithfulness and cancellation over Noetherian domains, Abelian groups that are torsion over their endomorphism rings, Abelian groups, Nearly isomorphic torsion free abelian groups, Direct sums of local torsion-free abelian groups, Modules with the quasi-summand intersection property, Torsion-free Abelian groups with hereditary rings of endomorphisms, A-Projective Resolutions and an Azumaya Theorem for a Class of Mixed Abelian Groups, Quasi-decomposition of abelian groups and Baer's lemma, Almost Completely Decomposable Torsion Free Abelian Groups, A Class of Pure Subgroups of Completely Decomposable Abelian Groups, Conductor of an Abelian group., Unnamed Item, E-transitive torsion-free Abelian groups, Faithful Abelian Groups of Infinite Rank, Warfield duality and rank-one quasi-summands of tensor products of finite rank locally free modules over Dedekind domains, Completely Decomposable Flat Modules over Locally Factorial Domains, Grothendieck rings for certain categories of quasihomomorphisms of torsion free modules over Dedekind domains, Duality and self-reflexive torsion-free Abelian groups, Reflexive rings and subrings of a product of Dedekind domains, The Jordan-Zassenhaus theorem and direct decompositions, The finite quasi-Baer property., The construction of $A$-solvable Abelian groups, Strongly Homogeneous Torsion Free Abelian Groups of Finite Rank, Countable \(\aleph _ 0\)-indecomposable mixed Abelian groups of finite torsion-free rank, Grothendieck and Whitehead groups of torsion free Abelian groups

Cites Work

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• Summands of finite rank torsion free abelian groups
• Homomorphisms and duality for torsion-free groups
• The classification of certain classes of torsion free Abelian groups
• Abelian groups without elements of finite order
• Grothendieck and Whitehead groups of torsion free Abelian groups
• Direct Products and Sums of Torsion-Free Abelian Groups
• Orders as Endomorphism Rings of Modules of the Same Rank
• On Quasi-Decompositions of Torsion Free Abelian Groups
• Every Countable Reduced Torsion-Free Ring is an Endomorphism Ring
• Torsion free groups of rank two