n-Gorenstein Projective Modules over Polynomial Rings

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。 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.