2024/06/14 by Yongliang Sun, Y. Zhang, Sun, Yongliang +1 · 1 citation
Mathematics · #16E65 #18G25 #18G65 #18G80 #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2406.09655
openalex publication_date 2024/06/14 · openalex created_date 2024/06/18 · openalex updated_date 2026/07/28
As an extension of Eisenbud's matrix factorization into the non-commutative realm, X.W. Chen introduced the concept of module factorizations over an arbitrary ring. A theorem of Chen establishes a triangle equivalence between the stable category of module factorizations with Gorenstein projective components and the stable category of Gorenstein projective modules over a quotient ring. In this paper, we introduce n-fold module factorizations, which generalize both the commutative n-fold matrix factorizations and the non-commutative module factorizations. To adapt triangle equivalences in module factorizations to n-fold module factorizations, we identify suitable subcategories of module factorizations and rings for the n-analogue. We further provide the n-analogue of Chen's theorem on triangle equivalences. Additionally, we study recollements involving the stable categories of higher-fold module factorizations, revealing intriguing recollements within the stable categories of Gorenstein modules of specific matrix subrings.