On a generalization of lifting modules relative to a torsion theory. (Q1949033)
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scientific article; zbMATH DE number 6157600
| Language | Label | Description | Also known as |
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| English | On a generalization of lifting modules relative to a torsion theory. |
scientific article; zbMATH DE number 6157600 |
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On a generalization of lifting modules relative to a torsion theory. (English)
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25 April 2013
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For a torsion theory \(\tau\) on the module category \(\text{Mod}(R)\) of right \(R\)-modules, a module \(M\) is called \(\tau\)-lifting if for any submodule \(N\) of \(M\) there exists a direct sum decomposition \(M=A\oplus B\), where \(A\subseteq N\) and \(N\cap B\) is \(\tau\)-small in \(M\). The authors establish several results concerning \(\tau\)-lifting modules, generalizing known properties of classical lifting modules.
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\(\tau\)-small submodules
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\(\tau\)-lifting modules
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torsion theories
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