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Generalized E-algebras via λ-calculus I

Rüdiger Göbel, Saharon Shelah (2006)

Fundamenta Mathematicae

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 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...

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.

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