Homomorphisms between $A$-projective Abelian groups and left Kasch-rings

Albrecht, Ulrich ; Jeong, Jong-Woo

Czechoslovak Mathematical Journal, Tome 48 (1998) no. 1, pp. 31-43.

Résumé

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 ${\mathrm{\Pi }}_p{A}_p$, and iii) $\mathrm{H}om(A,tA)$ 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.

Détail

Classification : 20K20, 20K21, 20K25, 20K30
Mots-clés : mixed Abelian group; endomorphism ring; Kasch ring; $A$-solvable group