多项式环上的n-Gorenstein投射模
n-Gorenstein Projective Modules over Polynomial Rings
DOI: 10.12677/PM.2025.156186, PDF,   
作者: 李夏妍：西北师范大学数学与统计学院，甘肃 兰州
关键词: n-Gorenstein投射模；n-Gorenstein内射模；多项式环；n-Gorenstein Projective Module； n-Gorenstein Injective Module； Polynomial Ring
摘要: 设n是一个正整数，R是环，本文讨论了多项式环上的n$-Gorenstein投射模和n-Gorenstein内射模的结构。证明了若(Y,f)是n-Gorenstein~投射左R[x]-模，则f是单同态，coker f是(n-1)-Gorenstein~投射左R-模；对偶地，(Y,f)是n-Gorenstein内射左R[x]-模，则f是满同态，Ker f是(n-1)-Gorenstein~内射左R-模。
Abstract: Let n be a positive integer and R be a ring. In this paper,n-Gorenstein projective modules and n-Gorenstein injective modules over polynomial rings were introduced.It is proved that if (Y,f) is an n-Gorenstein projective left R[x]-module, then f is a monomorphism and coker f is (n-1)-Gorenstein projective left R-module. Dually, if (Y,f) is an n-Gorenstein injective left R[x]-module, then f is an epimorphism and Ker f is (n-1)-Gorenstein injective left R-module.
文章引用：李夏妍. 多项式环上的n-Gorenstein投射模[J]. 理论数学, 2025, 15(6): 29-35. https://doi.org/10.12677/PM.2025.156186

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