Weakly tilting bimodules (Q2753154)
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scientific article; zbMATH DE number 1667147
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weakly tilting bimodules |
scientific article; zbMATH DE number 1667147 |
Statements
Weakly tilting bimodules (English)
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29 October 2001
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tilting modules
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categories of modules
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weakly tilting bimodules
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Brenner-Butler theorem
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The classical definition of a tilting module \(T\) (of projective dimension one) allows to identify the category of modules generated by \(T\) with a kernel of an \(\text{Ext}^1\)-functor and cogenerated modules with the kernel of a \(\text{Tor}_1\)-functor. The present article defines more general `weakly tilting bimodules' by replacing these equalities by inclusions (of the generated or cogenerated modules into the respective kernels). Many classical results such as the Brenner-Butler theorem have analogues in this setup. Related results can be found in another article by \textit{A. Tonolo} [J. Algebra 232, No. 1, 282-298 (2000; Zbl 0967.16003)].
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