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arXiv · 2203.08673

How to construct Gorenstein projective modules relative to complete duality pairs over Morita rings

Yajun Ma·Jiafeng Lü·Huanhuan Li·Jiangsheng Hu
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Abstract

Let $\Delta =\left(\begin{smallmatrix} A & {_AN_B}\\ {_BM_A} & B \\\end{smallmatrix}\right)$ be a Morita ring with $M\otimes_{A}N=0=N\otimes_{B}M$.We first study how to construct (complete) duality pairs of $\Delta$-modules using (complete) duality pairs of $A$-modules and $B$-modules, generalizing the result of Mao (Comm. Algebra, 2020, 12: 5296--5310) about the duality pairs over a triangular matrix ring. Moreover, we construct Gorenstein projective modules relative to complete duality pairs of $\Delta$-modules. Finally, we give an application to Ding projective modules.

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Yajun Ma, Jiafeng Lü, Huanhuan Li, Jiangsheng Hu. 2022-03-16. How to construct Gorenstein projective modules relative to complete duality pairs over Morita rings. https://doi.org/10.1142/s0219498824501536

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