A Ring is Right Finite Dimensional If It Contains No Infinite Direct Sum of Right Ideals. We Prove that If a Group G is Finite, Free Abelian, or Finitely Generated Abelian, then a Ring R is Right Finite Dimensional If and Only If the Group Ring RG is Right Finite Dimensional. a Ring R is a Self-Injective Cogenerator Ring If Rn is Injective and RR is a Cogenerator in the Category of Unital Right /{-Modules; This Means that Each Right Unital A-Module Can Be Embedded in a Direct Product of Copies of R. Let G Be a Finite Group Where the Order of G is a Unit in R. Then the Group Ring RG is a Selfinjective Cogenerator Ring If and Only If R is a Self-Injective Cogenerator Ring. Additional Applications Are Given. © 1973 American Mathematical Society.


Computer Science

Keywords and Phrases

Cogenerator; Complete ring of quotients; Dense right ideal; Group ring; Injective; Order; Rationally closed; Right finite dimensional

International Standard Serial Number (ISSN)

1088-6826; 0002-9939

Document Type

Article - Journal

Document Version


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Publication Date

01 Jan 1973