1. Homomorphisms between $A$-projective Abelian groups and left Kasch-rings
- Creator:
- Abrecht, Ulrich and Jeong, Jong-Woo
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- mixed Abelian group, endomorphism ring, Kasch ring, and $A$-solvable group
- Language:
- English
- Description:
- 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 $\Pi _p A_p$, and iii) $\mathop {\mathrm Hom}\nolimits (A,tA)$ 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public