Homomorphisms between A-Projective Abelian Groups and Left Kasch-Rings

Glaz and Wickless introduced the class G of mixed abelian groups A which have finite torsion-free rank and satisfy the following three properties: i) A_p is finite for all primes p, ii) A is isomorphic to a pure subgroup of _PA_P and iii) Hom(A, tA) is torsion. A ring R is a left Kasch ring if every proper right ideal of R has a non-zero left annihilator. We characterize the elements A of G such that E(A)/tE(A) is a left Kasch ring, and discuss related results.