环R与环R{X}上的模(英文)

Modules over R and R{X}

证明了w- 投射的w -模一定是自反模 ,得到在PVMD上每个有限型的w- 模都是自反模 .并证明了弱整体维数有限的凝聚整环一定是PVMD ,且其中的素w- 理想一定是平坦模 .同时 ,还建立w -operation的两个实现定理 ,即若R是SM整环 ,则R{X}是Noether整环 ;F是w 投射R 模 ,则F{X}是投射R{X} 模 .

In this paper, we show that every w-projective w-module is reflexive, moreover, every finite type w-module over a PVMD is reflexive. We also prove that a coherent domain with finite weak dimension is a PVMD in which every prime w-ideal is flat. Further, we obtain two representations of w-operation:if R is an SM domain, then R{X} is noetherian, and if F is w-projective as an R-module, then F{X} is projective as an R{X}-module.