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Frobenius functors and -torsionfree objects
Zhibing Zhao
We study -torsionfree objects in abelian categories with enough projectives. Frobenius functors preserve -torsionfreeness, and faithful ones reflect it. We prove that stabili…
The Grothendieck group of a triangulated category
Xiao-Wu Chen, Zhi-Wei Li, Xiaojin Zhang +1
We give a direct proof of the following known result: the Grothendieck group of a triangulated category with a silting subcategory is isomorphic to the split Grothendieck group of…
-torsionfree modules and Frobenius extensions
Zhibing Zhao
Let be a Frobenius extension and be a positive integer. We prove that an -module is -torsionfree if and only if so is its underlying -module. As an application,…
A non-vanishing result on the singularity category
Xiao-Wu Chen, Zhi-Wei Li, Xiaojin Zhang +1
We prove that a virtually periodic object in an abelian category gives rise to a non-vanishing result on certain Hom groups in the singularity category. Consequently, for any artin…
Gorenstein homological invariant properties under Frobenius extensions
Zhao Zhibing
We prove that for a Frobenius extension, a module over the extension ring is Gorenstein projective if and only if its underlying module over the base ring is Gorenstein projective.…