科研之友
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摘要
Let Lambda be a finite dimensional Auslander algebra. For a Lambda-module N, we prove that the projective dimension of N is at most one if and only if the projective dimension of its socle soc N is at most one. As an application, we give a new characterization of Auslander algebras. and prove that a finite dimensional algebra. is an Auslander algebra provided its global dimension gl.d Lambda <= 2 and an injective Lambda-module is projective if and only if the projective dimension of its socle is at most one.
- 出版日期2017-11
- 单位山东大学
