Krull整环与唯一分解整环上的自反模

Reflexive Modules over Krull Domains and UFDs

研究了Krull整环与唯一分解整环上的自反模,得到了若R是Krull整环,N是有限型的自反模F的自反子模,设I=(N:F)≠0,I有不可约的w-准素分解I=Q1∩…∩Qt,则N有唯一不可约的w-准素分解N=A1∩…∩At,使得Ai是自反的,且(Ai:F)=Qi,i=1,…,t.

In this article, we study mainly reflexive modules over Krull domains and UFDs. Let R be a Krull domain and N a reflexive suhmodule of a finite type reflexive module F. We show that if I = （N：F） ≠ 0 and 1 has an irreducible w-primary decomposition I=Q1∩…∩Qt, then N has a unique irreducible w-primary decomposition N=A1∩…∩At, such that Ai is reflexive and （Ai：F） =Qi, i = 1 ,… ,t. A similar result over UFDs is also proved.