Endomorphism rings of bimodules
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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.