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Two-sided E-rings

Authors
Journal
Journal of Pure and Applied Algebra
0022-4049
Publisher
Elsevier
Publication Date
Volume
185
Identifiers
DOI: 10.1016/s0022-4049(03)00090-2

Abstract

Abstract Let R be a ring, 1∈ R, and R + the additive group of R. We define Mult( R) to be the subring of End( R +) generated by all left and right multiplications by elements of R. The ring R is called a two-sided E-ring if End( R +)= Mult( R). If R is torsion-free of finite rank (tffr), we call R a quasi-two-sided E-ring if Q End(R +)= Q Mult(R) . We investigate (quasi)-two-sided E-rings, give several examples and construct large two-sided E-rings R with prescribed center S such that End( R +)= Mult( R)≈ R⊗ S R op ≈ R. Thus our rings R are examples of two-sided E-rings that are weak E-rings as well, i.e. R≈ End( R +), but R is not an E-ring.

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