A characterization of FGC rings.

DOI10.1216/rmjm/1181070035zbMath1042.13005OpenAlexW2131017982MaRDI QIDQ1415011

Peter Vámos, George Ivanov

Publication date: 3 December 2003

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/Vol32-4/CONT32-4/CONT32-4.html

zbMATH Keywords

endomorphism ringsdirect sum of cyclicsBaer-Kaplansky category

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Morphisms of commutative rings (13B10) Structure, classification theorems for modules and ideals in commutative rings (13C05) Commutative rings and modules of finite generation or presentation; number of generators (13E15)

Related Items (7)

Baer-Kaplansky classes of vector spaces and modules determined by numerical invariants ⋮ Baer-Kaplansky classes in Grothendieck categories and applications ⋮ The underlying vector spaces of certain endomorphism rings ⋮ Influence of the Baer-Kaplansky theorem on the development of the theory of groups, rings, and modules ⋮ Baer-Kaplansky classes in categories: transfer via functors ⋮ Baer-Kaplansky Theorem for Modules over Non-commutative Algebras ⋮ A Baer-Kaplansky theorem for modules over principal ideal domains

Cites Work

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• Generalizing the Baer-Kaplansky theorem
• Rings whose finitely generated modules are direct sums of cyclics
• Automorphism rings of primary abelian operator groups
• Modules Whose Lattice of Submodules is Distributive
• Decomposition of modules over serial rings
• Reduced rings whose finitely generated modules decompose
• The Decomposition of Finitely Generated Modules and Fractionally Self-Injective Rings
• A Krull-Schmidt Theorem for Infinite Sums of Modules
• Almost Maximal Valuation Rings

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