Abstract
Let be a -dimensional commutative Noetherian local ring. Let denote the morphism category of finitely generated -modules, and let be the full subcategory of consisting of monomorphisms, known as the submodule category. This article reveals that the Auslander transpose in the category can be described explicitly within , the category of finitely generated -modules. This result is exploited to study the linkage theory as well as the Auslander–Reiten theory in . In addition, motivated by a result of Ringel and Schmidmeier, we show that the Auslander–Reiten translations in the subcategories and , consisting of all morphisms which are maximal Cohen–Macaulay -modules and Gorenstein projective morphisms, respectively, may be computed within via -covers. The corresponding result for the subcategory of epimorphisms in is also obtained.
Citation
Abdolnaser Bahlekeh. Ali Mahin Fallah. Shokrollah Salarian. "Specifying the Auslander transpose in submodule category and its applications." Kyoto J. Math. 59 (1) 237 - 266, April 2019. https://doi.org/10.1215/21562261-2018-0010
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