Relative Transpose and its Dual with Respect to a Bimodule |
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Authors: | Guoqiang Zhao |
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Institution: | 1.Department of Mathematics,Hangzhou Dianzi University,Hangzhou,People’s Republic of China |
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Abstract: | For a class of modules \(\mathcal {X}\), we introduce the \(\mathcal {X}\)-transpose of a module with respect to a bimodule, which unifies some well-known transposes. Let \(\mathcal {V}\) be a subclass of \(\mathcal {X}\). The relations between \(\mathcal {X}\)-transposes and \(\mathcal {V}\)-transposes are investigated under the condition that \(\mathcal {V}\) is a generator or cogenerator of \(\mathcal {X}\). The dual aspects of \(\mathcal {X}\)-transposes are also discussed. Then we give some applications of these results. In particular, the dual counterparts of Gorenstein transposes are established. |
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