In this paper,we study extended modules for a special class of Oreextensions.We will assume that R is a ring and A will denote the Ore extensionA:=R[X1,...,xn;σ]for whichσis an automorphism of R,xixj=xjxi and xir=σ...In this paper,we study extended modules for a special class of Oreextensions.We will assume that R is a ring and A will denote the Ore extensionA:=R[X1,...,xn;σ]for whichσis an automorphism of R,xixj=xjxi and xir=σ(r)xi,for every 1<i,j≤n.With some extra conditions over the ring R,wewill prove Vaserstein's,Quillen's patching,Horrocks',and Quillen-Suslin's theoremsfor this type of non-commutative rings.展开更多
基金the project New trends of non-commutative algebra and skew PBW extensions,HERMES CODE 26872,Universidad Nacional de ColombiaThe authors are grateful tothe editors and the referee for valuable suggestions and corrections.
文摘In this paper,we study extended modules for a special class of Oreextensions.We will assume that R is a ring and A will denote the Ore extensionA:=R[X1,...,xn;σ]for whichσis an automorphism of R,xixj=xjxi and xir=σ(r)xi,for every 1<i,j≤n.With some extra conditions over the ring R,wewill prove Vaserstein's,Quillen's patching,Horrocks',and Quillen-Suslin's theoremsfor this type of non-commutative rings.
