I proved that $\mathbb Q$ is not finitely generated as $\mathbb Z$-module using Nakayama Lemma. Now I want to prove the following:     $\mathbb Q$ is not finitely generated as $\mathbb Z$- algebra.   I don't want to use the result that: A field which is finitely generated $\mathbb Z$-algebra is finite.  Any help will be appreciated. Many thanks.
Suppose $k$ is a field that is finitely generated as a ${\mathbb Z}$-algebra.  (That is, $k$ is a quotient of ${\mathbb Z}[X_1,\dots,X_n]$ for some $n$). Does it follow that $k$ is finite?
My 5 year- old daughter is constantly defiant! My 5-year old daughter is very defiant.  It started getting bad about 6 months ago. She doesn't do what she is told, and any time she hears the word "no" she throws terrible, dramatic fits, screaming ridiculously loud, and in some cases hitting.  She refuses to make eye contact when I warn her to stop doing something even when I am down at her eye level and it takes multiple orders to finally get her to look at me. She constantly tells me no.  I feel like I constantly tell her no and that she feels this gives her the right to tell her father and I no.  I have tried time outs which are not effective at all; she only throws a fit the whole time, never seeming to run out of wind. Spankings are only effective until the shock of the action itself wears off and then she returns to the same behavior.  My husband and I recently took away ALL of her toys/ possessions being she is a pretty materialistic child (she loves getting toys and always wants something new). We told her that if she was good and listened and stopped telling us no and throwing fits, that after three days we would let her choose three boxes of toys to bring back in her room. This worked but as soon as she got those three boxes unpacked, we packed them back up because she went right back to the no's and fit-throwing within a few hours.  I am mainly the one disciplining her and I feel she is definitely the most defiant with me. I believe in explaining to her why things are not OK and why I tell her no, but I really don't feel it helps and I never feel as if she listens to what I tell her.  I am at my wits' end and feel like a failure of a mother. She is my first and only child, and the only grandchild on both sides of our family. She is an angel at school but home is completely different.  I need help figuring this out but nobody I talk to really has any advice for me. I am at the point where I am wondering if she or I need counseling because I feel out of options. Geometry dash lite to Geometry dash full version I currently have the Geometry Dash lite version and I want to buy the full version. Can I login with my account of Geometry Dash lite and keep everything I already had? It would suck if I had to redo everything. I have a typical scientific manuscript in a LaTeX .tex file, and I need to convert it to MS Word .doc file.  The reason for having to convert to MS Word is I'm submitting the manuscript to an academic journal and they only accept MS Word (I know...)  The manuscript includes title page, figures, tables, equations (inline and in their own align environment), footnotes, bibliography, and an annex.  The tables are in their own separate tables.tex file, which I include using the \include{tables} command.  Most tables take up a whole landscape page, and were generated sing the package pdflscape.  I am using Windows 7 Professional.    My plan is to use pandoc to go from .tex to .odt, open the latter in Libre Office, and convert to .doc.  I have read a related  but it is too general.  Similarly the examples in the Pandoc  are too simple.  I have played around but I am unable to accomplish what I want.  This is surprising since converting a scientific manuscript is probably the most common use case for Pandoc. Here are some sample failures:  Example 1  I open a command line in the project folder, and execute the following:  pandoc -s document.tex -o document.odt   I get this error message:  pandoc: figure1: openFile: does not exist &lt;no such file or directory&gt;   where figure1 is the name of a figure file (e.g. figure1.png) in the project folder referenced in a line as \includegraphics[width=5.8in]{figure1}.  I suspect pandoc expects a .png extension but not sure how to provide it.  Example 2  Next I try .html, and excute the following:  pandoc -s document.tex -o document.html   The program executes fine.  I open HTML file.  Footnotes are there but figures are missing, tables are displayed as LaTeX, bibliography is missing, in-line math displays well, but math in align environment does not, section labels are displayed, and some other minor issues.  So given that mine is probably a typical use case scenario, my question is this: What commands should I use to get the .odt file I want?  I could not find a fully worked out example on the web.    Here is a specific list of errors.  I'll update how I corrected them based on community suggestions:   Figures not rendering.  Solved by adding .png extension to .tex file in \includegraphics command.  Now figures are included but they are huge, with half of each figure outside the page. No bibliography.  Solved. First, I have one huge consolidated Latex .bib file where I keep all my citations.  I manage it using .  This was giving me problems as I do not keep the cleanest .bib file in town.  So I reduced the problem by using a neat trick in JabRef that allows you to subset your master .bib file using the .aux file generated by Latex when compiling your manuscript.  In JabRef click on Tools > New Subdatabase based on AUX file.  This way I generated a much smaller biblio.bib file with only the articles referenced in my manuscript.  Running pandoc -s document.tex -o document.odt --bibliography=biblio.bib did the trick. Display math. Math in \begin{align} environment displayed in verbatim \latex;  (A partial solution is to use the  Libre Office extension.  Copy and paste the latex math code in the .odt file created by Pandoc into the equation editor, and so on.  Surely this could be built into a macro that can post-process all remaining math.)  UPDATE: Display math works very well using --mathjax extension. Inline math. Inline equation do not always render properly.  Bold math is a problem.  E.g. $\Sigma=\sigma^2\bm{I}$ displays as $\Sigma=\sigma^2\bm{I}$; Labels are displayed (e.g. section labels show as [sec:empirical] blah blah]; All tables display as raw latex. Maximum Likelihood Estimate with different parameters Suppose that X and Y are independent Poisson distributed values with means $\theta$ and $2\theta$, respectively. Consider the combined estimator of $\theta$ $$ \tilde{\theta} = k_1 X + k_2 Y $$ where $k_1$ and $k_2$ are arbitrary constants.   Find the condition on $k_1$ and $k_2$ such that $\tilde{\theta}$ is an unbiased estimator of $\theta$. For $\tilde{\theta}$ unbiased, show that the variance of the estimator is minimized by taking $k_1 = 1/3$ and $k_2 = 1/3$. Given observations $x$ and $y$ find the maximum likelihood estimate of $\theta$ and hence show that $\tilde{\theta}$ is also the maximum likelihood estimator.   I have gotten (1) and (2) okay, but it's (3) I am having trouble with, I'd be okay if $X$ and $Y$ had the same parameter but I'm having trouble with $X$ and $Y$ having different parameters, any help would be appreciated.   NOTE   For (1) I got $k_1 = 1 - 2k_2$.   For (2) I found the variance of $\tilde{\theta}$, then differentiated and let equal to zero to minimize - therefore we get (after subbing in $k_2 = 1 - k_1/2 $) $$3k_1-1=0,$$ which when subbing in $1/3$, we see it is minimised.   Thank you. I read this story 30+ years ago in grade school. A man crashes on an alien planet. He has a small amount of water and accidentally spills some, and the planet replicates it but it must destroy part of itself to do so.  The man then finds some stale crumbs in his pocket, puts them in a trough, and the planet replicates them as well, but it's disgusting to eat. The man eventually decides that his situation is hopeless, so he lays down to die on a table in a hot room and thinks he can at least give back to the planet some of the nutrients it sacrificed for him. He falls asleep, and when he awakens, he has been transformed into an alien creature that is perfectly suited and adapted to live on the planet without discomfort to himself or damage the planet. What are some CD Ripping Programs you can use on Ubuntu? What are some CD ripping programs for Ubuntu? Can you list the Pros? What are the Cons? For each program there should be a screenshot, sources to install, and instructions to install and use. How to create a filter in Gmail to identify messages forwarded from Zimbra? iPhone 5S, LTE does not work Selecting attribute values with html Agility Pack I'm trying to retrieve a specific image from a html document, using html agility pack and this xpath:  //div[@id='topslot']/a/img/@src   As far as I can see, it finds the src-attribute, but it returns the img-tag. Why is that?  I would expect the InnerHtml/InnerText or something to be set, but both are empty strings. OuterHtml is set to the complete img-tag.  Are there any documentation for Html Agility Pack? I am trying to create an spritz app. Everything was working fine, but since yesterday I keep getting this error:     ./spritz: line 176: syntax error: unexpected end of file   I have checked the script file and everything seems perfect. I am confused, I have an if statement at last and it looks correct! Here is the last portion:  #checks if speed is 150 157 if [[ $2 -eq 150 ]]; 158 then 159 starttime=$SECONDS 160      FS=$'\n' 161      for j in `grep --color=always -iP '\b[^aeiou\s]*[aeiou][^aeiou\s]*\K[aeiou]' $1`; 162      do 163            #Reads the text file in the centre of the screen 164            echo "                                                    ___________________" 165            echo "                                                             $j"; 166            echo "                                                    ___________________" 167            echo "                                                                               Speed 150 wpm" 168            sleep  0.9; 169            clear; 170       done 171 endtime=$(($SECONDS - $starttime)) 172            echo "You read $words_read words in $endtime seconds!" 173       exit 8 174 fi   What could cause that error? my 4 week old daughter will not stop crying. We've tried everything from sucking, both on pacifiers and fingers to breastfeeding, white noise, movement, diaper is clean she doesn't seem to have a fever.   We've tried everything we can read about and think of.  We are both a little bit ill, the common cold and the baby may have gotten it and be upset but we are just at the end of our nerves when nothing helps our poor little one!   Does anyone know anything we can do to help? I need to include a couple of Python code listings, where the indentation of the lines (using some number of spaces) is significant. I would like for the code listings to be copyable, so the spaces at the beginning of the line need to be be copied along with the text.  This question has been asked in various ways before (e.g. , or ). Those questions focus on making line numbers uncopyable, though.  Making the spaces at the beginning of a line copyable seems to be harder: "I am not sure it is possible to specify in the PDF (at least in a viewer-independent way) that the indentation should be copied too" (). At , Philippe Goutet suggests a solution (turning the spaces into visible spaces, and coloring them in the background color so that they appear invisible) that works using Acrobat Reader, but not all readers. He says "It works under Acrobat Reader and it's extremely pleasant to be able to quickly copy/paste code without problem (perhaps the problem can be circumvented by writing direct PDF code to tell that it's a space, I've never had the time to try)".  Is it possible to produce a PDF with a code listing with copyable real spaces at the beginning of a line?  Minimal example: The line return x should start with four spaces.  \documentclass{article}  \begin{document} \begin{verbatim} def myfunction(x):     return x \end{verbatim} \end{document}   I know that I could attach the code to the PDF as a file, but that's not what I want. How does one attack a two-time pad (i.e. one time pad with key reuse)? What are 'closures' in .NET? What is a closure? Do we have them in .NET?  If they do exist in .NET, could you please provide a code snippet (preferably in C#) explaining it? I need to add 30 minutes to values in a Oracle date column.  I do this in my SELECT statement by specifying   to_char(date_and_time + (.000694 * 31)  which works fine most of the time.  But not when the time is on the AM/PM border.  For example, adding 30 minutes to 12:30 [which is  PM] returns 1:00 which is AM. The answer I expect is 13:00.  What's the correct way to do this? How to prove that: $\tan(3\pi/11) + 4\sin(2\pi/11) = \sqrt{11}$ Why doesn't the Moon fall onto the Earth? For that matter, why doesn't anything rotating a larger body ever fall onto the larger body? Bash shell script output alignment My script:  date echo -e "${YELLOW}Network check${NC}\n\n"  while read hostname do  ping -c 1 "$hostname" &gt; /dev/null 2&gt;&amp;1 &amp;&amp;  echo -e "Network $hostname : ${GREEN}Online${NC}" || echo -e "${GRAY}Network $hostname${NC} : ${RED}Offline${NC}"  done &lt; list.txt         sleep 30 clear done   Is outputting info like this:    Network 10.x.xx.xxx : Online    Network 10.x.xx.xxx : Offline    Network 10.x.xx.xxx : Offline    Network 10.x.xx.xxx : Offline    Network 10.x.xx.x : Online    Network 139.xxx.x.x : Online    Network 208.xx.xxx.xxx : Online    Network 193.xxx.xxx.x : Online   which I'd like to clean up to get something like this:    Network 10.x.xx.xxx       : Online   Network 10.x.xx.xxx       : Offline    Network 10.x.xx.xxx       : Offline     Network 10.x.xx.x         : Online     Network 139.xxx.x.x       : Online   Network 208.xx.xxx.xxx    : Online     Network 193.xxx.xxx.x     : Online   Network 193.xxx.xxx.xxx   : Offline Inspecting standard container (std::map) contents with gdb Supposing to have something like this:  #include &lt;map&gt; int main(){     std::map&lt;int,int&gt; m;     m[1] = 2;     m[2] = 4;     return 0; }   I would like to be able to inspect the contents of the map running the program from gdb. If I try using the subscript operator I get:    (gdb) p m[1] Attempt to take address of value not located in memory.   Using the find method does not yield better results:  (gdb) p m.find(1) Cannot evaluate function -- may be inlined   Is there a way to accomplish this? UK Visa has been refused for false document