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The almost split sequences for the Morita context. (Chinese. English summary) Zbl 1313.16015

Summary: Let \(\Lambda_1,\Lambda_2\) be rings, \(M\) be a \((\Lambda_2\)-\(\Lambda_1)\)-bimodule and \(N\) be a \((\Lambda_1\)-\(\Lambda_2)\)-bimodule. The six-tuple \(\Gamma=(\Lambda_1,\Lambda_2,N,M,\psi,\varphi)\) is a Morita context. In order to study the representations of \(\Gamma\), it is important to determine its almost split sequences (i.e., AR-sequences). The authors construct the corresponding morphisms in \(\Gamma\) through the right (left) almost split morphisms and the irreducible morphisms in \(\text{mod\,}\Lambda_1\) and \(\text{mod\,}\Lambda_2\). Furthermore, its almost split sequences are determined.

MSC:

16D90 Module categories in associative algebras
16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
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