I have a very simple question. Suppose that $A$ is a (commutative) Dedekind domain, $B$ is a subring of $A$ and $P$ is a nonzero prime ideal of $A$. Is it true that the prime ideal $P\cap B$ of $B$ is also nonzero? Thank you.
Let $B$ be a commutative domain and $A \subseteq B$ a subring. Suppose that the extension $A \to B$ is finite, i.e. $B$ is finitely generated as an $A$-module. If $I \cap A = \lbrace 0 \rbrace$ for some ideal $I$ of $B$, can we conclude that $I = \lbrace 0 \rbrace$?  I know that if $I$ contains a nonzero prime ideal, the statement holds since $A \to B$ is an integral extension, whereby no two comparable prime ideals of $B$ can have the same intersection with $A$. But does the statement still hold if $I$ does not contain a nonzero prime ideal? And what if $A \to B$ is only assumed to be an integral extension?
How do I get my Sony A7 II to avoid over-exposure and look more like my Canon camera? Hai.  I have a question, I switched from Canon to Sony a while ago and I found out that if I shot bright places, like the sky, the cloud that is supposed to be seen clearly, looks like a blown-out highlight (like real crazy), as you can see on my picture.  I have to set a low exposure just so the highlight is not blown out, and it’s only happening on Sony, not on Canon. On Canon the object is visible, but the background (cloud) is still seen all just fine.  Do you guys know what to change on the Sony to get that good look? Is it the setting or the lens? (BTW, I’m using a Sony 35mm f/1.8 lens.) How can I integrate $$\ln \left( x+\sqrt{1+x^2} \right) $$   The problem is from IA Maron Calculus, Problem 4.3.17. The problem is under the heading 'Integration by parts'. I have tried it, but it just leads to 2 unsolvable integrals In Problems in Mathematical Analysis, Volume 2 by Kaczor and Nowak, Problem 2.3.34 is stated as follow.   Find this limit using L`Hôpital rule  $$\lim\limits_{x\to\infty}x((1+\frac{1}{x})^x-e).$$  I have tried by using L'Hospital rule five times but have no result.  I can compute this limit by using Taylor expansion. Idempotent of closure and other properties What's the meaning of a set to the power of another set? What's the use of a decoupling capacitor near a reservoir capacitor? I've seen some circuits where a decoupling capacitor is used as well as a reservoir capacitor, like this (C4 and C5):    I've read about  and for me it looks as if they are meant to remove small fluctuations in the supply voltage. Then I thought - wasn't that the purpose of a  as well? Why wouldn't the reservoir capacitor be able to filter out the small fluctuations, if it is able to filter out the large fluctuations?  So I feel like I have a basic misunderstanding here. What is the purpose of a decoupling capacitor next to a reservoir capacitor, when we assume we place both equally near to the power consuming part? Or is the only advantage of the decoupling capacitor that it is smaller and can therefore be easily placed more near to the power consuming part? What is the most ruby-ish way of accessing nested hash values at arbitrary depths? Calculate Euler equations of fluid dynamics without division? About the anime version of Air:  Some sources on the net state that Kanna's curses were broken, and her next reincarnation would be a happy one.  Some say that the pair of children playing on the beach were the reincarnations of Misuzu-Kanna / Yukito-Ryūya.  What is the canonical explanation of this ending? Did the curses really get lifted? Please include sources in your answer. What does the helpful flag mean? I don't see "Helpful" in the list of things I can do when I press the flag link.   In my profile page I saw "6 helpful flags."  How do I earn these flags?  May I make them on other peoples' posts or comments?   This is what I am talking about: Is there a difference between "Joe said" and "said Joe"? Does the subject/verb order make a difference when writing a dialog tag?  &quot;The sky is blue,&quot; Joe said. &quot;The sky is blue,&quot; said Joe.  Is one preferable over the other? Does one emphasize the speaker (or the method of speech, such as shout) more than the other? (Personally, I would use the second form to emphasize that Joe made the statement) How to take the gradient of the quadratic form? It's stated that the gradient of:  $$\frac{1}{2}x^TAx - b^Tx +c$$  is   $$\frac{1}{2}A^Tx + \frac{1}{2}Ax - b$$  How do you grind out this equation? Or specifically, how do you get from $x^TAx$ to $A^Tx + Ax$? Difference between ' and " on command line (bash)? I have not idea how to approach this differential equation.   $$y'-\int_0^xy(t)dt=2$$.  Basically, I did,  $$F''(t)-F(x)+F(0)=2 \;\;\;\;\;\;\; F'=y$$  I am stuck.  Thank You. This afternoon I set up a Win Server 2008 R2 system for use with Team Foundation source code control. In order to give my team-mates the right to connect, I had to create a user account for each person, 10 in total. (I can't, and I don't want to create a domain).  Now, after doing this, all user accounts are displayed in the login screen.  What can I do so that all the accounts are not displayed there? How can I add a class to a block with code (development) For theming reasons I'd like to add a specific class at the "block" level to some of the blocks I'm generating with a custom module. I know there is a module , but I would rather like to do it directly in code (there is no need to change is afterwards).   I also know of , but that does not seem to allow adding or editing classes.  Is it possible to add a class with to a block from within my module code? I'm using Drupal 7. Why must we "avoid discussions in comments"? I've just started getting these messages:     Please avoid extended discussions in comments. Would you like to automatically move this discussion to chat?   Why should one avoid doing this? I think it adds to the site...  (Tagged  in more ways than one!) Making ArcPy interactive? What is an "Emergency Call," and can I  set number for it? How to fix slow wireless on machines with Intel wireless cards?