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A degeneration-like order for modules

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Abstract.

Let A be a finite dimensional algebra over an algebraically closed field. In [4] Riedtmann has proved that for any exact sequence \(0\to N\to M\oplus Z\to Z\to 0\) of finite dimensional A-modules, M degenerates to N. We prove that the relation \(M\leq\! _RN\) defined by the existence of the above sequence is a partial order on the set of isomorphism classes of finite dimensional A-modules.

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Received: 23.10.1997

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Zwara, G. A degeneration-like order for modules. Arch. Math. 71, 437–444 (1998). https://doi.org/10.1007/s000130050288

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  • DOI: https://doi.org/10.1007/s000130050288

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