科研之友
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摘要
Let R be a left and right Noetherian ring. In this paper, we prove that any Gorenstein transpose of a finitely generated R-module is exactly an Auslander transpose. As applications, we obtain a new relation between a Gorenstein transpose of a module with a transpose of the same module, and show that the Gorenstein transpose of a module is unique up to Gorenstein projective equivalence. In addition, when R is an Artin algebra, the corresponding Auslander-Reiten sequences are constructed in terms of Gorenstein transposes.
