Nilpotent elements of a quotient ring
Find the nilpotents in $\mathbb{Z}_3[x]/(x^2-1)$
Why do some games allow offline Steam achievements? I know of  where it is asked if you can get Steam achievements offline. The accepted answer to that was no.   But I do earn achievements for some Steam games while playing in offline mode!  For example, right now I am earning achievements for Cave Story+ as I play in offline mode. In other games I also earn achievements while playing in offline mode. Not just when I am disconnected but still in "online" mode as might be suggested in the linked question.  But what is really bugging me is that this does not happen with all games that have Steam achievements.  So, is allowing offline achievements something that Steam allows, the game devs allow, or is it something decided by a magical elf in the steam servers rolling some d20 dice around?  Edit:  As per request, I was able to attain visual evidence:    You should be able to see the achievement-get in action while in offline mode.  What is worth noting, (and something that I forgot to mention before) is that I only started earning achievements after I had went into online mode with the game installed. This is why I was able to earn this achievement with the ones after unlocked. I had started the game for the first time in offline mode, and did not notice that I was not earning achievements. When I had connected once, I did not have to start the game while online. I was able to earn achievements offline.  I also must state publicly: I do not play on easy. This was for testing purposes only people. It was for Science! List has no rows for assignment to SObject How to change kernel at boot I installed the latest kernel (4.1) and want to boot into it instead of 3.9. How can i do this on ubuntu 15.04? Java error: Implicit super constructor is undefined for default constructor Over the past couple of days there have been a few questions about overlapping proposals and questions that could belong on multiple sites:        What is the best practice before / after asking a question if you think your question might be better on another site?  or  If I think my question might belong on multiple sites as per the above posts? Questions about a commutative ring with exactly three ideals Let $R$ be a commutative ring with identity. Assume that $R$ has exactly three distinct ideals: $\{0\},I, R.$      1) Show that if $a \in R-I$, then $a$ is a unit in $R$.      2) Let $a,b\ne0$ in $I$. Show that $ab=0$. Proof of property of abelian group Can you use external money to pay trading commissions in tax-free and tax-deferred accounts? How to use hook_node_presave to change field's value Basically, I want to put first name &amp; surname together into $node->field_par_contact_name  But it gives me warning. (See below)   function partnership_node_presave($node) {   if($node->type == 'partnership') {     $first_name = $node->field_par_contact_first_name['und'][0]['name'];     $surname = $node->field_par_contact_surname['und'][0]['name'];      // https://drupal.org/project/field_hidden     // Hidden variable     $node->field_par_contact_name['und'][0]['value'] = $first_name. ' '. $surname;      // Warning after save: array_flip(): Can only flip STRING and INTEGER values! in DrupalDefaultEntityController->load() (line 173 of .../drupal-7.23/includes/entity.inc   } }   Updated, please see image: How to show a group is cyclic? One question asking if $\mathbb{Z}^*_{21}$ is cyclic.  I know that the cyclic group must have a generator which can generate all of the elements within the group.  But does this kind of question requires me to exhaustively find out a generator? Or is there any more efficient method to quickly determine if a group is a cyclic group? Is the function $f(x)=|x|^{1/2}$ Lipschitz continuous near $0$? If yes, find a constant for some interval containing $0$.   I think the answer is yes since I can find $L=1$ that satisfies Lipschitz continuity criteria in a interval close to $0$, am I right? The characteristic and minimal polynomial of a companion matrix I am using \if condition in a custom command in my LaTeX document. I would like to know where I can find some good explanation about \if command. I followed a  but it's just an example; there are not any explanation. Some conditions require that a person lie in bed all the time until recovered. Is there a name for such conditions or people experiencing them at the moment?   For example,      I am currently &lt;bed sick&gt; and can't help you with your homework.   I tried looking for bed sick but hit a dead end. dpkg-divert: error: rename involves overwriting `/usr/lib/xorg/protocol.txt' with different file `/usr/lib/xorg/protocol-precise.txt', not allowed Is 512 bits a more secure hashing than 256 bits? Taylor Series type inequality Why would parametric statistics ever be preferred over nonparametric? Can someone explain to me why would anyone choose a parametric over a nonparametric statistical method for hypothesis testing or regression analysis?   In my mind, it's like going for rafting and choosing a non-water resistant watch, because you may not get it wet. Why not use the tool that works on every occasion? Product rule intuition Can anyone think of an intuitive explanation of the product rule? I'm not asking for a derivation. To me it seems like quite an un-untuitive result, as apposed to the chain-rule (which is ironically harder to derive). How to remove the left part of a string? I have some simple python code that searches files for a string e.g. path=c:\path, where the c:\path part may vary. The current code is:  def find_path(i_file):     lines = open(i_file).readlines()     for line in lines:         if line.startswith("Path="):             return # what to do here in order to get line content after "Path=" ?   What is a simple way to get the text after Path=?