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Wakamatsu Tilting Modules, $U$-Dominant Dimension and $k$-Gorenstein Modules

Zhaoyong Huang
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Abstract

Let $Λ$ and $Γ$ be left and right noetherian rings and $_ΛU$ a Wakamatsu tilting module with $Γ={\rm End}(_ΛT)$. We introduce a new definition of $U$-dominant dimensions and show that the $U$-dominant dimensions of $_ΛU$ and $U_Γ$ are identical. We characterize $k$-Gorenstein modules in terms of homological dimensions and the property of double homological functors preserving monomorphisms. We also study a generalization of $k$-Gorenstein modules, and characterize it in terms of some similar properties of $k$-Gorenstein modules.

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Zhaoyong Huang. 2006-09-18. Wakamatsu Tilting Modules, $U$-Dominant Dimension and $k$-Gorenstein Modules. https://arxiv.org/abs/math/0409150

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