A domain $R$ is a Dedekind domain iff it is integrally closed, Noetherian with Krull dimension at most one. I think they put Noetherian in the definition not only to make proofs easier but also because it's important. To see that it's really necessary to have Noetherian in the definition do you have an example for me of a domain $R$ which is integrally closed, not Noetherian with Krull dimension one? All my examples of domains which are not Noetherian fail to have Krull dimension one.
I've tried to construct examples of rings that match all except one of the properties in the definition of a Dedekind domain. (This is an old number theory qual question from Berkeleys MGSA website).  The only starting point that I can think of would be  $R:=K[X_1,X_2,\ldots]$  for $K$ a field. This is clearly integrally closed as any polynomial relation is contained in $K(X_1,\ldots,X_n)$ for some large enough $n$ and $K[X_1,\ldots,X_n]$ is integrally closed being a UFD.  The problem is then to get rid of enough ideals from this ring $R$, so that its dimension would be 1, but I can't seem to figure out what to do.  Anyone have any other ideas for rings that could work as a starting point? The polynomial ring with an infinite number of variables is pretty much the only example that I know of for how to construct a non-noetherian ring that's still a domain.
How do you mark a struct template as friend? How do you perform a left outer join using linq extension methods Assuming I have a left outer join as such:  from f in Foo join b in Bar on f.Foo_Id equals b.Foo_Id into g from result in g.DefaultIfEmpty() select new { Foo = f, Bar = result }   How would I express the same task using extension methods? E.g.  Foo.GroupJoin(Bar, f =&gt; f.Foo_Id, b =&gt; b.Foo_Id, (f,b) =&gt; ???)     .Select(???) What advantages does using (function(window, document, undefined) { ... })(window, document) confer? Why is 'ping' unable to resolve a name when 'nslookup' works fine? On my Windows XP workstation, I can find the machine I want to connect to in DNS with nslookup:  nslookup wolfman Server: dns.company.com Address: 192.168.1.38  Name: wolfman.company.com Address: 192.168.1.178   But, when I try to connect to that machine, I get an error telling me that the machine can't be found (i.e., can't be looked up in DNS):  C:\&gt; ping wolfman Ping request could not find host wolfman. Please check the name and try again.   I am able to connect if I use the IP address directly:  C:\&gt; ping 192.168.1.178  Pinging 192.168.1.178 with 32 bytes of data:  Reply from 192.168.1.178: bytes=32 time=41ms TTL=126 Reply from 192.168.1.178: bytes=32 time=41ms TTL=126 Reply from 192.168.1.178: bytes=32 time=44ms TTL=126 Reply from 192.168.1.178: bytes=32 time=38ms TTL=126   I could work around this by adding an entry to my hosts file, but I would rather find out why this is happening.  The problem is transient, most of the day I can connect to the machine just fine.  How is this possible?  ETA: I left this out for brevity, but it was asked for:  C:\&gt; ping wolfman.company.com Ping request could not find host wolfman.company.com. Please check the name and try again.   ETA: Other applications get the same results.  I only tried ping to simplify.  telnet can't connect, Cygwin apps print a "unknown host wolfman" message.  Update: Using wireshark, I found that my workstation is not attempting a DNS lookup.  It's just reporting the "could not find host" error message. Developing Unit Tests While Refactoring Legacy Code? What is the expression on RegularExpressionValidator to check if the Textbox text is 6 or more characters long? Can a child inherit both their parents' clans jutsu? Can a child in Naruto inherit both abilities from his parents' clans?  For example, if Ino and Sasuke had a child is there a possibility for it to have both Uchiha's Sharingan and Yamanaka's mind transfer jutsu? IBM Slack links broken Deleting a middle node from a single linked list when pointer to the previous node is not available Is it possible to delete a middle node in the single linked list when the only information available we have is the pointer to the node to be deleted and not the pointer to the previous node?After deletion the previous node should point to the node next to deleted node. Anonymous Internet browsing Could you please suggest me a good anonymous internet browsing application for Ubuntu? When to use "have" and "have got" tput: No value for $TERM and no -T specified I am trying to run a bash script I have via cron, and I am getting the following error at the beginning of the execution:  tput: No value for $TERM and no -T specified   Here is what is in my crontab:  0 8 * * 1-5 cd /var/www/inv/ &amp;&amp; /var/www/inv/unitTest run all 2&gt;&amp;1| mail -r "user@example.com" -s "Daily Inventory Unit Test Results" user@example.com How do I Deserialize this XML document:  &lt;?xml version="1.0" encoding="utf-8"?&gt; &lt;Cars&gt;   &lt;Car&gt;     &lt;StockNumber&gt;1020&lt;/StockNumber&gt;     &lt;Make&gt;Nissan&lt;/Make&gt;     &lt;Model&gt;Sentra&lt;/Model&gt;   &lt;/Car&gt;   &lt;Car&gt;     &lt;StockNumber&gt;1010&lt;/StockNumber&gt;     &lt;Make&gt;Toyota&lt;/Make&gt;     &lt;Model&gt;Corolla&lt;/Model&gt;   &lt;/Car&gt;   &lt;Car&gt;     &lt;StockNumber&gt;1111&lt;/StockNumber&gt;     &lt;Make&gt;Honda&lt;/Make&gt;     &lt;Model&gt;Accord&lt;/Model&gt;   &lt;/Car&gt; &lt;/Cars&gt;   I have this:  [Serializable()] public class Car {     [System.Xml.Serialization.XmlElementAttribute("StockNumber")]     public string StockNumber{ get; set; }      [System.Xml.Serialization.XmlElementAttribute("Make")]     public string Make{ get; set; }      [System.Xml.Serialization.XmlElementAttribute("Model")]     public string Model{ get; set; } }   .  [System.Xml.Serialization.XmlRootAttribute("Cars", Namespace = "", IsNullable = false)] public class Cars {     [XmlArrayItem(typeof(Car))]     public Car[] Car { get; set; }  }   .  public class CarSerializer {     public Cars Deserialize()     {         Cars[] cars = null;         string path = HttpContext.Current.ApplicationInstance.Server.MapPath("~/App_Data/") + "cars.xml";          XmlSerializer serializer = new XmlSerializer(typeof(Cars[]));          StreamReader reader = new StreamReader(path);         reader.ReadToEnd();         cars = (Cars[])serializer.Deserialize(reader);         reader.Close();          return cars;     } }   that don't seem to work :-( What is "my guy syndrome" and how do I handle it? I've been reading forum posts and blogs who mention "my guy" syndrome as a specific type of difficult player, but I can't seem to find a solid definition for the term. Can someone explain this particular kind of problem player to me? How do you deal with this kind of problem? How to put small numbers outside the pie slices without making a mess I'm new to LaTeX and need some help with my figures. I would like to to put small numbers outside the pie slices without making a mess. Having found this thread , I tried it out, but didn't get all the way through with it. Right now, my pie looks like this:    I used the following code:  \usepackage{tikz,stackengine} \makeatletter  \tikzstyle{chart}= [legend label/.style={font={\scriptsize},anchor=west,align=left}, legend box/.style={rectangle, draw, minimum size=5pt}, axis/.style={black,thin,-&gt;}, axis label/.style={anchor=east,font={\tiny}}]  \tikzstyle{bar chart}=[ chart, bar width/.code={     \pgfmathparse{##1/2}     \global\let\bar@w\pgfmathresult}, bar/.style={thin, draw=black}, bar label/.style={font={\bf\small},anchor=north}, bar value/.style={font={\footnotesize}}, bar width=.75,]  \tikzstyle{pie chart}= [chart, slice/.style={line cap=round, line join=round, thin, draw=black}, pie title/.style={font={}}, slice type/.style 2 args={     ##1/.style={fill=##2},     values of ##1/.style={}}]  \pgfdeclarelayer{background} \pgfdeclarelayer{foreground} \pgfsetlayers{background,main,foreground}  \newcommand{\pye}[3][]{     \begin{scope}[#1]         \pgfmathsetmacro{\curA}{90}         \pgfmathsetmacro{\r}{1}         \def\c{(0,0)}         \node[pie title] at (270:1.3) {#2};         \foreach \v/\s in{#3}{             \pgfmathsetmacro{\deltaA}{\v/100*360}             \pgfmathsetmacro{\nextA}{\curA + \deltaA}             \pgfmathsetmacro{\midA}{(\curA+\nextA)/2}             \path[slice,\s] \c             -- +(\curA:\r)             arc (\curA:\nextA:\r)             -- cycle;             \pgfmathsetmacro{\d}{max((\deltaA * -(.5/50) + 1) , .5)} %%%              %\pgfmathprintnumberto{#3}{\fnum}  %\ifthenelse{\lengthtest{#3 pt &lt; 10pt}} %{\path (O) -- ++ (\midangle:\radius) %node[inner sep=0,align=left,anchor=west,rotate=\midangle](nums#3)    {~~\fnum};} %{\path (O) -- ++(\midangle:\innerpos)  %node {\scalefont{#3}\beforenumber\fnum\afternumber};}           %%%                         \begin{pgfonlayer}{foreground}                 \path \c -- node[pos=\d,pie values,values of \s]{$\v\%$} +    (\midA:\r);             \end{pgfonlayer}             \global\let\curA\nextA}     \end{scope}}  \newcommand{\legend}[2][]{     \begin{scope}[#1]         \path         \foreach \n/\s in {#2}         {++(0,-5pt) node[\s,legend box] {} +(2pt,0) node[legend label]     {\n}};     \end{scope}}      \begin{document}         \begin{center}      \begin{figure}[H]     \centering \begin{tikzpicture} [pie chart, slice type={A}{black!0}, slice type={B}{black!10}, slice type={C}{black!20}, slice type={D}{black!30}, slice type={E}{black!40}, slice type={F}{black!50}, slice type={G}{black!60}, slice type={H}{black!70}, pie values/.style={font={\small}}, scale=2]  \pye{1994}{6.1/A, 2.9/B, 0.2/C, 54.3/D, 25.2/E, 1.4/F, 6.7/G, 3.2/H} \pye[xshift=2.2cm,values of coltello/.style={pos=1.1}]% {2005}{6.8/A, 3.0/B, 0.5/C, 52.3/D, 25.6/E, 1.8/F, 7.1/G, 2.8/H} \pye[xshift=4.4cm,values of caffe/.style={pos=1.1}]% {2015}{7.2/A, 3.1/B, 0.6/C, 50.6/D, 26.5/E, 2.3/F, 7.5/G, 2.2/H}  \legend[shift={(0cm,-1.5cm)}]{{A}/A, {B}/B}  \legend[shift={(1.4cm,-1.5cm)}]{{C}/C, {D}/D}  \legend[shift={(2.8cm,-1.5cm)}]{{E}/E, {F}/F} \legend[shift={(4.2cm,-1.5cm)}]{{G}/G, {H}/H} \end{tikzpicture} \end{figure}  \end{document}   This looks quite the way I want it to, only the small numbers should be placed outside the pies.  Thanks in advance :) I am getting a warning when trying to include the .net 3.5 sp1 prerequisite for my setup project.  The warning states Prerequisite could not found for bootstrapping.  Any suggestions?  Thanks Proving that closed (and open) balls are convex I am a new user of Ubuntu 12.04.   I installed Ubuntu and Windows XP, and I want to use both operating systems. When I restart or boot my PC the GRUB menu does not appear.  How can I solve this problem? How to find users by name Brief Description:  I need my Ethernet card (en0) to see all traffic under 192.168.2.xxx.  However I also need to use WiFi card (en1) for all other traffic.  OS: OS X Lion    I am using a separate network location to deal with this specific use (since this is a for a robotics project that communicates via Ethernet). Ethernet (en0) had to be set up as a static IP (192.168.2.10) per the requirements for the device I am connecting to. All connections on the Ethernet card (en0) should be 192.168.2.xxx as specified above. WiFi (en1) is set up as DHCP to a router since their is no point in assigning it as a static for general purpose traffic. Ethernet (en0) is set up as priority over WiFi (en1).  I would also like to keep this under the network location preferences if at all possible since I do not require this feature to be on all the time.  I would really appreciate your help on this. No one I have talked to knows how to solve this.