Extension functors on the category of \(A\)-solvable abelian groups. (English) Zbl 0776.20018

Let \(A\) and \(G\) be abelian groups. The group \(H_ A(G)=\operatorname{Hom}(A,G)\) has an \(E(A)\)-module structure in the natural way. Conversely, we set \(T_ A(M)= M\otimes_{E(A)}A\) for any right \(E(A)\)-module \(M\). The group \(G\) is said to be \(A\)-solvable, if the natural evaluation map \(\theta_ G: T_ A H_ A(G)\to G\) is an isomorphism. The author investigates some extension functors on the category \(C_ A\) of \(A\)-solvable groups. The methods developed are used for a construction of \(A\)-solvable groups in the case that \(A\) is slender and has rank at least two.
Reviewer: L.Bican (Praha)


20K40 Homological and categorical methods for abelian groups
16S50 Endomorphism rings; matrix rings
20K35 Extensions of abelian groups
20K30 Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups
Full Text: EuDML


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