A-Projective Resolutions and an Azumaya Theorem for a Class of Mixed Abelian Groups

DOI10.1023/A:1013753704818zbMath1079.20503OpenAlexW1488674895MaRDI QIDQ3366554

Ulrich F. Albrecht

Publication date: 14 February 2006

Published in: Czechoslovak Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/30616

zbMATH Keywords

direct sumsprojective groupsdirect productsdirect summandspure subgroups\(A\)-generated groups\(\mathcal A\)-decomposable groups\(\mathcal G_{\mathcal A}\)-presented groups

Mathematics Subject Classification ID

Homological and categorical methods for abelian groups (20K40) Direct sums, direct products, etc. for abelian groups (20K25) Subgroups of abelian groups (20K27) Mixed groups (20K21)

Related Items (13)

Homological Properties of Quotient Divisible Abelian Groups ⋮ Fuchs’ problem 34 for mixed Abelian groups ⋮ The quasi-Baer-splitting property for mixed Abelian groups. ⋮ SELF-SMALL ABELIAN GROUPS ⋮ Direct sums of self-small mixed groups ⋮ Purity and Self-Small Groups ⋮ Quasi-decompositions for Self-Small Abelian Groups ⋮ \(sp\)-groups and their endomorphism rings ⋮ A-Solvability and Mixed Abelian Groups ⋮ Homomorphisms between A-Projective Abelian Groups and Left Kasch-Rings ⋮ A Note on FinitelyA-Presented Abelian Groups ⋮ Self-small mixed abelian groupsGwithG/T(G) finite rank divisible ⋮ The finite quasi-Baer property.

Cites Work

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• Projective modules
• Endomorphism rings of faithfully flat Abelian groups
• Global Azumaya theorems in additive categories
• The flat dimension of mixed abelian groups as \(E\)-modules
• A flatnes s criterion in Grothendieck categories
• Abelian groups without elements of finite order
• Endomorphism Rings and Direct Sums of Torsion Free Abelian Groups
• Regular and principal projective endomorphism rings of mixed abelian groups
• The construction of $A$-solvable Abelian groups
• Every Cotorsion-Free Ring is an Endomorphism Ring

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