Cyclic Ext (Q2639968)

Let the abelian p-group G be decomposed as a direct sum \(B\oplus D\) of a reduced group B and a divisible group D. Consider G as a module over its endomorphism ring E. In an earlier paper [Math. Z. 89, 77-81 (1965; Zbl 0131.254)], the authors showed how to recover the E-module G from the ring structure of E in the cases where B is unbounded or \(D=0\). The missing case in which B is unbounded and \(D\neq 0\) was handled by \textit{R. Kuebler} and \textit{J. D. Reid} [Rocky Mt. J. Math. 5, 585-592 (1975; Zbl 0333.20047)]. This paper presents a simplified derivation of Kuebler and Reid's result. It also contains two generalizations of Kuebler and Reid's theorem that \(Ext_ E(B,D)\) is cyclic over the center of E.