拟Ω-整环的若干性质

Some Properties of The Quasi-Ω-Domains

摘要: 文章首先给出了拟Ω-整环的定义,同时对拟Ω-整环提出了两个问题,并给出了肯定的回答,最后还证明了若R是一个PVMD的拟Ω-整环,则对R的每个非零的素w-理想P来说,或者ω-L(y)(ω-F(P))=ω-P^↓,或者ω-L(ω-F(P))=ω-P^↓\P且P是未分支的.

Abstract: In this paper the defin ition of the quas i-Ω-domains is given.Then two questions about the quasi-Ω-domains are put forward and the affirmative reply is given.It is proved that if R is a quasi-Ω-domain with PVMD,then ω-L(ω-F(P))=ω-P^↓,or ω-L(ω-F(P))=w-P^↓\P with P being unbranched foreach nonzero prmie idealw-ideal P of R.