If $K$ is a field is $K[X^2,X^3]$ a UFD when considered as a subring of $K[X]$?   I know that $K[X]$ is a $PID$ but nothing else ,these ring theory question just dont seem to occur to me..please help...someone told me it is not a $UFD$ and only just a Domain...but i dont know the reason..how should one go about proving these results?..this ring theory course is getting to hard for my understanding..
Show that $X^2$ and $X^3$ are irreducible but not prime in $K[X^2,X^3]$.   My reasoning is as follows:  Since the only ways $X^2$ and $X^3$ can be factored in $K[X^2,X^3]$ are $X^2 = X^2 * 1$ and $X^3=X^3*1$ it follows that $X^2$ and $X^3$ are irreducible.  To show that they are not prime in $K[X^2,X^3]$ I argue that $X^2\mid X^3*X^3$ but $X^2\nmid X^3$ and $X^3\mid X^4*X^2$ but $X^3\nmid X^4$ or $X^3\nmid X^2$.  Is that correct?
given value of matrix, getting it's coordinate I have a couple of illustrations done in Illustrator and I am planing to animate it for a website that I am working on, I've heard of  toolkit with flash, but is it the best way to go or is there another "better" way of doing it?  Here's an example of the kind of animations I am aiming for: Bibliography error: "Use of \blx@bbl@verbadd@i doesn't match its definition. \verb" Currently having problems with compiling my Master's thesis after downloading the newest version of TeXStudio and MiKTeX. The error message is as follows:  Use of \blx@bbl@verbadd@i doesn't match its definition. \verb   The only other place I found a similar question regarding this error message was found here:   I am not sure how this applies to my problem, but from what I understand this is due to some problem in an external file. If you need the bibliography-entry, I can provide you with that on short notice, though it is rather long (which is why I didn't include it here in the first place).  I am using Mendeley Desktop v1.16.1 to automatically generate my BibTeX database.   I am using biblatex as follows:  \usepackage[backend = bibtex,         style = numeric-comp,         sorting = none,         natbib = true,         doi = false,         isbn = true,         hyperref = true]{biblatex}   I also have some code to change how the bibliography output, but I doubt it is causing the problem, as commenting it out did not help.  Hope anyone knows what causes my problem and how to fix it.  Thanks. How can I visualize or simulate the effect of different focal lengths? I have seen many camera review sites illustrate the effect of using different focal lengths on the same photograph using frames. There are also similar illustrations to compare different sensors (). I find this kind of visualization to be very useful in comparing the actual effect of the longer focal length\different sensor size. Of course the ability to do a wider focal length visualization would also be equally useful, but that's not possible.  Is there any ready-made software or plugin that enables this? If not, is there any simple technique to visualize the effect of longer focal lengths on an image (one would of course have to use the zoom information in the image EXIF data to accurately represent this)? All I can think of is to use some trigonometry to do the necessary calculations for the frame sizes for cropping. Move every file that is not a directory Why a line is said to have infinite number of points? Samba authentication fails How to determine whether a given Linux is 32 bit or 64 bit? When I type uname -a, it gives the following output.  Linux mars 2.6.9-67.0.15.ELsmp #1 SMP Tue Apr 22 13:50:33 EDT 2008 i686 i686 i386 GNU/Linux   How can I know from this that the given OS is 32 or 64 bit?  This is useful when writing configure scripts, for example: what architecture am I building for? Are {/bin, /lib, /sbin} symlinks into /usr in Ubuntu? I do not have access to an Ubuntu system or chroot. I was hoping if someone could tell me if the  is accurate in saying:     For Quantal, merged /usr should be supported. On new systems installer should create {/bin, /lib, /sbin} symlinks into /usr. I have a problem with this file tex:  \begin{document} \begin{figure} \begin{center} \begin{pspicture}(0,0)(1,3.8) \psline{-&lt;}(0,0)(0,.2) \psline{-}(0,.2)(0,.4) \psline{*-&gt;}(0,.4)(0,.9) \psline{-*}(0,.9)(0,1.4) \psline{-&lt;}(0,1.4)(0,2.4) \psline{-}(0,2.4)(0,3.4) \psline{*-}(0,3.4)(0,3.6) \psline{&gt;-}(0,3.6)(0,3.8) \rput(1,.4){$y=0$}%testo \rput(1,1.4){$y=1$} \rput(1,3.4){$y=3$} \end{pspicture} \end{center} \caption{} \end{figure} \end{document}   but I don't understand where is the error. What's the difference between &lt;div class=""&gt; and &lt;div id=""&gt; when it comes to CSS? Is it alright to use &lt;div id=""&gt;?  I see different developers doing this in both ways, and since I'm self taught, I've never really figured it out. Troubleshooting for biber Value of recommendation letters from professors in a different field How to Count Duplicates in List with LINQ Change this behavior to allow for spelling corrections and the like: "Edits must be at least 6 characters" I'm using python in QGIS. I have a layer of polygons (its a result of some earlier dissolving and has no overlapping polygons but some holes and islands in holes etc). I want to build a new layer which contains one polygon representing a bbox of the first layer with each polygon cut from it.  Essentially I want to "invert" the layer I have so that where the was polygon, now there is not, and where there was not polygon now there is. All inside a bounding box of the original layer.  I can build a bbox easily and I tried to "subtract" the polygon layer from my new bbox polygon layer but the process slows to a stop and then crashes my PC. Here's the algorythm  processing.runalg("qgis.difference","path/to/polygon.shp","path/to/bbox.shp","path/to/result.shp")   I dont care about attributes (obviously). I just need to cut one set of polygons from one larger polygon.  It seems so simple, I wish I could find a simple command or script to acheive this. As stated at the top I'm looking for a solution in python in QGIS. I want to install the latest Firefox on my Ubuntu (64bit) box.  What is the best way to do this? Is there a specific update site or should I download the binaries manually? If doing manually, in which directory should I put the files? In my home directory, or is there a better place? What does "Package  has no installation candidate" mean? What does the above Error mean? What is an installation candidate?  I was trying to do  sudo apt-get install munin-memcached     and I get this message:  Reading package lists... Done Building dependency tree        Reading state information... Done Package munin-memcached is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source E: Package munin-memcached has no installation candidate   I googled for the problem and someone said to do a apt-get upgrade but it still did not solve my problem. Will yearly moderation statistics be published on all sites this year, and future years? I am trying to integrate one Salesforce org to other org by using Oauth setup, I wanted to use  use consumer key and consumer secret key in my REST class to connect with the org, after connection part completion, I want to access Get(), Put(), Post(), etc. Including the ability to set Oauth and Authorization headers needed for Salesforce Rest API calls.  Actually I'm new in REST implementation so can you please explain me by using code samples.