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Morita contexts and torsion theories. (English) Zbl 0835.16005

For a Morita context \((R, V, W, S)\) and a hereditary torsion theory \(\tau\) on Mod-\(R\), the author constructs a hereditary torsion theory \(\underline {\tau}\) on Mod-\(S\) and points out that for a suitable hereditary torsion theory \(\lambda\) on Mod-\(R\), the quotient categories Mod-\((R,\lambda)\) and Mod-\((S, \underline {\tau})\) are equivalent. He also shows that for suitable rings \(R\) and \(S\), there exists a context \((R, V, W, S)\) such that the correspondence \(\tau \to \underline {\tau}\) is well-behaved in the sense that if for example \(\tau\) is the Goldie torsion theory then so is \(\underline {\tau}\).

MSC:

16D90 Module categories in associative algebras
16S90 Torsion theories; radicals on module categories (associative algebraic aspects)
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