Let $M$ be an abelian group and let $R = \mbox{End}\_\Bbb{Z}(M)$. Under what conditions (on $M$), $\_RM$ is injective!?



Abelian groups injective over their endomorphism
It seems that such modules where classified by Fred Richman and Elbert A. Walker, in *Modules over PIDs that are injective over their endomorphism rings*, Ring Theory (Proc. Conf., Park City, Utah, 1971), p.363-372, Academic Press, N.-Y., 1972.


The paper is available on [E. A. Walker's website](http://www.math.nmsu.edu/~elbert/#publications). 


