Zhibing Zhao

activity

20172026

most citedThe Grothendieck group of a triangulated category

1 citations · 1 across the 9 of their papers we have counts for

collaborators

9 papers

math.RT2026

Frobenius functors and $n$ -torsionfree objects

Zhibing Zhao

We study $n$ -torsionfree objects in abelian categories with enough projectives. Frobenius functors preserve $n$ -torsionfreeness, and faithful ones reflect it. We prove that stabili…

math.RA2024

Wakamatsu tilting modules and Frobenius extensions

Yanhong Bao, Jiafeng Lü, Zhibing Zhao

Let $S / R$ be a Frobenius extension with $_{R} S_{R}$ centrally projective over $R$ . We show that if $_{R} ω$ is a Wakamatsu tilting module then so is $_{S} S \otimes_{R} ω$ , and the natural ring…

math.RT2024★ 1 cited

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…

math.RT2023

$k$ -torsionfree modules and Frobenius extensions

Zhibing Zhao

Let $R / S$ be a Frobenius extension and $k$ be a positive integer. We prove that an $R$ -module is $k$ -torsionfree if and only if so is its underlying $S$ -module. As an application,…

math.RT2023

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…

math.RA2020

Cohomological invariants of algebraic operads, I

Yan-Hong Bao, Yan-Hua Wang, Xiao-Wei Xu +3

We study various invariants, such as cohomology groups, derivations, automorphisms and infinitesimal deformations, of algebraic operads and show that $A ss$ , $\mathcal{C}c…

math.RA2019

Multiplicative derivations on rank- $s$ matrices for relatively small $s$

Xiaowei Xu, Baochuan Xie, Yanhua Wang +1

Let $n$ and $s$ be fixed integers such that $n \geq 2$ and $1 \leq s \leq \frac{n}{2}$ . Let $M_{n} (K)$ be the ring of all $n \times n$ matrices over a field $K$ . If a m…

math.RA2018

$X$ -Gorenstein projective dimensions

Zhibing Zhao, Xiaowei Xu

In this paper, we mainly investigate the $X$ -Gorenstein projective dimension of modules and the (left) $X$ -Gorenstein global dimension of rings. Some properti…

math.RT2017

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.…

Frobenius functors and n-torsionfree objects

Wakamatsu tilting modules and Frobenius extensions

The Grothendieck group of a triangulated category

k-torsionfree modules and Frobenius extensions

A non-vanishing result on the singularity category

Cohomological invariants of algebraic operads, I

Multiplicative derivations on rank-s matrices for relatively small s

X-Gorenstein projective dimensions

Gorenstein homological invariant properties under Frobenius extensions

Frobenius functors and $n$ -torsionfree objects

$k$ -torsionfree modules and Frobenius extensions

Multiplicative derivations on rank- $s$ matrices for relatively small $s$

$X$ -Gorenstein projective dimensions