$ \omega $-left approximation dimensions under stable equivalences of adjoint type

Juxiang Sun; Weimin Liu; Juxiang Sun; Weimin Liu

doi:10.3934/math.2025893

AIMS Mathematics

2025, Volume 10, Issue 9: 19994-20009. doi: 10.3934/math.2025893

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$ \omega $-left approximation dimensions under stable equivalences of adjoint type

Juxiang Sun ¹,
Weimin Liu ^{2
,
,}

1.
School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, China
2.
Department of Physics, Shangqiu Normal University, Shangqiu 476000, China

Received: 15 April 2025 Revised: 21 August 2025 Accepted: 25 August 2025 Published: 01 September 2025
MSC : 16E30, 18G25

In this paper, we study invariant properties of $ \omega $-left approximation dimensions of modules under the stable equivalences of adjoint type. As applications, we prove that Wakamatsu tilting modules, Wakamatsu tilting conjectures, relative $ n $-torsionfree modules, and generalized Gorenstein dimensions of modules are preserved under those equivalences.
- $ \omega $-left approximation dimension,
- faithful dimension,
- Wakamatsu tilting module,
- Wakamatsu tilting conjecture,
- stable equivalence of adjoint type
Citation: Juxiang Sun, Weimin Liu. $ \omega $-left approximation dimensions under stable equivalences of adjoint type[J]. AIMS Mathematics, 2025, 10(9): 19994-20009. doi: 10.3934/math.2025893

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Abstract

In this paper, we study invariant properties of $ \omega $-left approximation dimensions of modules under the stable equivalences of adjoint type. As applications, we prove that Wakamatsu tilting modules, Wakamatsu tilting conjectures, relative $ n $-torsionfree modules, and generalized Gorenstein dimensions of modules are preserved under those equivalences.

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