Об абелевых группах без кручения с наследственными кольцами эндоморфизмов

П.А. Крылов

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The lattice R-tors for perfect rings.

H. A. Rincón Mejía (1989)

Publicacions Matemàtiques

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Some torsion theoretical characterizations of rings.

Ahsan, Javed (1984)

International Journal of Mathematics and Mathematical Sciences

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

Ulrich F. Albrecht, Jong-Woo Jeong (1998)

Czechoslovak Mathematical Journal

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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 $Π_{p} A_{p}$ , and iii) $H o m (A, t A)$ 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 $E (A) / t E (A)$ is a left Kasch ring, and discuss related results.