Endomorphism rings of bimodules |
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Authors: | Ulrich Albrecht Rüdiger Göbel |
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Institution: | 1. Department of Mathematics, Auburn University, Auburn, AL, ?36849, USA 2. Fakult?t für Mathematik, Universit?t Duisburg-Essen, 45117, ?Essen, Germany
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Abstract: | Let \(M\) be an \(R\) - \(R\) -bimodule over a semi-prime right and left Goldie ring \(R\) . We investigate how non-singularity conditions on \(M_R\) are related to such conditions on \(_RM\) . In particular, we say an \(R\) - \(R\) -bimodule \(M\) such that \(_RM\) and \(M_R\) are non-singular has the right essentiality property if \(IM_R\) is essential in \(M_R\) for all essential right ideals \(I\) of \(R\) , and investigate several questions related to this property. |
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