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Dualities and the duality density theorems. (Q1031859)

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scientific article; zbMATH DE number 5620124
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English
Dualities and the duality density theorems.
scientific article; zbMATH DE number 5620124

    Statements

    Dualities and the duality density theorems. (English)
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    23 October 2009
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    The paper deals mainly with particular non-degenerating \(_RK_D\)-pairing (i.e., a bilinear product) of a left \(R\)-module \(_RS\) and a right \(D\)-module \(T_D\) with values in an \(R\)-\(D\)-bimodule \(K\). The main situation considered is that when certain additional properties on \(R\), \(S\), \(K\), \(T\) allow an application of techniques, ideas, methods of (not necessarily finite dimensional) dual vector spaces developed in Jacobson's famous book ``Structure of rings''. However, the presentation seems to be ad hoc although the now standard language of Morita equivalence and duality could be suitable.
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    non-degenerate pairings
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    dualities
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    semisimple algebras
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