PVMD的拟Ω-整环

The Quasi-Ω-Domains With PVMD

摘要: 描绘了一个PVMD的拟Ω-整环.证明了若R是一个PVMD的拟Ω-整环,则R的每个非零素ω的非ω-g理想是未分支的;对R的一个素ω-理想P来说,或者ω-D(ω-J(P))=ω-P^↓,或者w-D(ω-J(P))=ω-P^↓\P,P是未分支的.同时,还证明了若R是一个PVMD的拟Ω-整环,P和N是R的不可比的素w-理想,设J=∩Q|Q∈)w-N^↓\ω-P^↓,则J是一个素ω-理想,且.

Abstract: We characterize a quasi-Ω-domains with PVMD.And we prove that if R is a quasi-Ω-domain with PVMD,then ω-D(ω-J(P))=ω-P^↓,or ω-D(ω-J(P))=w-P^↓Pwith P being unbranched for each nonzero prime ω-ideal P of R.And then we prove that if R is a quasi-Ω-domain with PVMD,P and N are two incomparable prime ω-ideals of R,and J=∩Q|Q∈ω-N^↓\ω-P^↓,then J is a prime w-ideal,and .