Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 2 down vote favorite

Let $R$ be a Prufer domain with quotient field $K$ and $\sum$ be the set of all semilocal Prufer domains $R'$ with $n$ maximal ideals and quotient field $K$ such that $R\subseteq R'$. Let $R=R'_{1}\cap\ldots\cap R'_{t}$ where $R'_{1},\ldots,R'_{t}$ are minimal elements of $\sum$ (ordered by inclusion) and pairwise incomparable. Is $\{R'_{1},\ldots,R'_{t}\}$ the set of all minimal elements of $\sum$ ?

Thanks for your answers.

share|improve this question
I can't see any reason for choosing $5$ instead of an arbitrary positive number $t$. – YACP Jan 15 at 20:46
1  
I don't think this question deserves to be closed. – YACP Jan 15 at 21:00
1  
I vote to keep this question open. – QiL'8 Jan 15 at 22:54
you re right. you can put any finite number t instead of 5 – Azadeh Jan 16 at 9:48
Let me ask this question in general case: Let $R$ be a integral domain with quotient field $K$. Let $\sum$ be the set of all overrings of R (a subring of $K$ containing $R$). Assume that $R=R_{1}\cap\ldots\cap R_{t}$ ($t$ is finite) where $R_{1},\ldots,R_{t}$ are minimal elements of $\sum$ (ordered by inclusion) and $R_{1},\ldots,R_{t}$ are pairwise incomparable by inclusion. Is $\{R_{1},\ldots,R_{t}\}$ the set of all minimal elements of $\sum$ ? – Azadeh Jan 16 at 10:05

Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.