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An R-algebra A is called an E(R)-algebra if the canonical homomorphism from A to the endomorphism algebra $E n d_{R} A$ of the R-module $_{R} A$ , taking any a ∈ A to the right multiplication $a_{r} \in E n d_{R} A$ by a, is an isomorphism of algebras. In this case $_{R} A$ is called an E(R)-module. There is a proper class of examples constructed in [4]. E(R)-algebras arise naturally in various topics of algebra. So it is not surprising that they were investigated thoroughly in the last decades; see [3, 5, 7, 8, 10, 13, 14, 15, 18, 19]. Despite...

Generating solutions of some Cauchy and cosine functional equations.

Maciej Sablik (1987)

Aequationes mathematicae

Green's relations and regular elements of transformation semigroups

Igor Kossaczký (1987)

Mathematica Slovaca

Groups qui reflètent les décompositions de leurs quotients ou de leurs sous-groups

Khalid Benabdallah, Robert Bradley (1977)

Revista colombiana de matematicas

Groups with finite conjugacy classes of subnormal subgroups

Carlo Casolo (1989)

Rendiconti del Seminario Matematico della Università di Padova

Hereditary endomorphism rings of mixed Abelian groups.

Krylov, P.A. (2002)

Sibirskij Matematicheskij Zhurnal

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

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

Czechoslovak Mathematical Journal

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.