I'm a bit confused. Consider the following situation:  We know $M^{2\times 2}(\mathbb{Z})$ has an identity for $\cdot$ which is $$e_1 =\begin{pmatrix}  1 &amp; 0 \\ 0 &amp; 1 \\ \end{pmatrix}.$$ Now consider the subring $$A = \left\{\begin{pmatrix}  x &amp; 0 \\ 0 &amp; 0 \\ \end{pmatrix}\mid x \in \mathbb{Z}\right\},$$ which has identity element:$$e_2 =\begin{pmatrix}  1 &amp; 0 \\ 0 &amp; 0 \\ \end{pmatrix}.$$  In my book on algebra, it says that if $1\in R$ and $S\subset R$ is a subring of $R$, then $1\in S$ needs to be met. But in this example, this is not the case. Can someone help with my confusion?
Is there an example of a ring $S$ with identity $1_S$ containing a non-trivial subring $R$ which itself has an identity $1_R$, but $1_R\neq 1_S$ (or equivalently $1_S\notin R$). I'd also like to know under what conditions the identities have to be equal. I know they must be equal if $S$ has no zero divisors, since for every $r\in R$ we have $(1_S-1_R)r=0$  In other words: Is the category of unital rings with identity-preserving morphisms a full subcategory of the category of rings (where morphism are only required to respect addition and multiplication)?
Replaced wrong car in garage in GTA Online How do I disable overlay scrollbars? It looks like Ubuntu 11.04 will come with  by default. I do like them, but I don't like the current mix of scrollbar types as many applications don't yet use those overlay scrollbars.  Is there a way to disable overlay scrollbars (without removing the overlay-scrollbar package)? Allow folding/collapsing of certain segments of posts A question with attachments, screenshots and/or long code, makes it vertically long and often difficult to read fast.  It would be nice to have a new kind of format, such as 'hideable', with a graphic button or a '+' / '-' sign, so you can add additional details, visible only on a click. Getting two pictures to appear on the same page Whenever I create a document in Microsoft Word, it complains about a lot of my sentences being in passive voice. But, when I read that sentence aloud, it sounds fine to me. I am not sure if it is just me and will a statement in passive voice sound strange to a native speaker?  So, my question is, is it considered bad form to use passive voice generally? Or in some specific cases like written communications only?  Edit: If it is ok to use passive voice, then why does MS-Word complain? Changing default \citet font in biblatex I'm using biblatex to manage my citation in a natbib style :  \usepackage[style=alphabetic,maxnames=6,natbib=true]{biblatex}   However when I use the \citet command, the author's name is in a \textsc font, I would like to change this behavior so that the font used is the default one, but I could not find how to do this in biblatex's documentation. I wanna create a new partition from the existing root partition.My root partition is about 250GB.I wanna create a new partition say 150 GB taking space from this root partition.Can anyone help me with the procedure on doing this?  output: fdisk -l  karthick@karthick:~$ sudo fdisk -l [sudo] password for karthick:   Disk /dev/sda: 250.0 GB, 250000000000 bytes 255 heads, 63 sectors/track, 30394 cylinders Units = cylinders of 16065 * 512 = 8225280 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x28219744  Device Boot      Start         End      Blocks   Id  System /dev/sda1   *           1          61      487424   83  Linux Partition 1 does not end on cylinder boundary. /dev/sda2              61       30395   243650561    5  Extended /dev/sda5              61         124      498688   82  Linux swap / Solaris /dev/sda6             124         186      498688   82  Linux swap / Solaris /dev/sda7             186       30395   242651136   83  Linux How to prepare files for rsync on a case insensitive filesystem? Relative Pronouns are ALWAYS added right after antecedent? Is is a rule that relative clauses should be added right after the antecedent(the noun relative pronouns refer to)? What if it is confusing?   For example:  "I went for a spin with a handsome boy last night."  "The handsome boy went out with my friend."  "I went for a spin with a handsome boy who went out with my friend last night ."  "I went for a spin with a handsome boy last night who went out with my friend." Can RUBIK's cube be solved using group theory? If yes, how can we use it to solve a $2\times2$ Rubiks Cube? How do I save the output of a command to a file?  Is there a way without using any software? I would like to know how. Is there a way of creating a filesystem object akin to this:  mknod files p cat file1 file2 ... fileN &gt; files   but such that it can be seeked in, as if it were a regular file? Expected value of $|X - Y|$ Let $X \sim U(0, 1)$ and $Y \sim U(0, 2)$ be independent random variables. What's the expected value of $|X - Y|$? I found $f_{X}(x) = 1$ and $f_{Y} = \frac{1}{2}$ so that $f_{XY}(x, y) = \frac{1}{2}$ and $$\mathbb{E}[|x - y|] = \int_{0}^{1} \int_{0}^{2} \frac{|x - y|}{2} \mathop{dy} \mathop{dx},$$ but how can I compute this quantity? It looks tricky. I know the trick where you split the integral in the one-dimensional case, but I'm having trouble getting it in the two-dimensional case. I don't really get why these hyperbolic functions are named after trig functions. Can someone enlighten me? Resize multiple layers around their respective anchor points I have 50 or so layers (imported images as smart objects) that I would like to scale down, while they stay in place. Is there a way of doing this? I know After Effects has, is there a similar Scale property in photoshop? Accidentally hit "toggle full screen", How do I exit? I'm stuck in full screen in the node editor. Escape isn't working, and I have no menus and no idea how to leave except to quit Blender and reopen the program. Preface: Every couple of days there comes a question of this type, which is easy to solve with sed, but takes time to explain. I'm writing this question and answer, so I can later refer to this generic solution and only explain the adaption for the specific case. Feel free to contribute.  I have files with variable definitions. Variables consist of uppercase letters or underscore _ and their values follow after the :=. The values can contain other variables. This is Gnom.def:  NAME:=Gnom FULL_NAME:=$FIRST_NAME $NAME FIRST_NAME:=Sman STREET:=Mainstreet 42 TOWN:=Nowhere BIRTHDAY:=May 1st, 1999   Then there is another file form.txt with a template form:  $NAME Full name: $FULL_NAME Address: $STREET in $TOWN Birthday: $BIRTHDAY Don't be confused by $NAMES   Now I want a script which replaces the variables (marked with $ and the identifier) in the form by the definitions in the other file, recursively, if necessary, so I get this text back:  Gnom Full name: Sman Gnom Address: Mainstreet 42 in Nowhere Birthday: May 1st, 1999 Don't be confused by $NAMES   The last line is to ensure that no substrings of variables get replaced accidentally. "Element is no longer attached to the DOM” StaleElementReferenceException when selecting HTML table row I am using Selenium 2/WebDriver for automation. I have a table and am trying to select a row in it. When the test runs, I can see the row become highlighted as if it is clicked, but then immediately I get the "org.openqa.selenium.StaleElementReferenceException: Element is no longer attached to the DOM" error and the test fails.  The code is the following:  @Test public void rowSelection() throws Exception {     SeleniumHelper helper = new SeleniumHelper();     action = new SeleniumActionHelper(driver);      helper.login();      String testUrl = navigateToUrl("option/listOptions.xhtml");     driver.get(testUrl);      WebElement table = findElementById("tableSection:dataTableWrapped_data");     List&lt;WebElement&gt; allRows = table.findElements(By.tagName("tr"));     for (WebElement row : allRows)         {             List&lt;WebElement&gt; cells = row.findElements(By.tagName("td"));             for (WebElement cell : cells)             {                 WebElement listName = cell.findElement(By.xpath("./* [text()='body_build']"));                 listName.click();             }         } }   I have put a Thread.sleep(2000) in front and after the listName.click() action, but neither has helped. Any help would be greatly appreciated. Does the faction of your armor/clothes affect character interactions in Skryim? Story about a utopian city that periodically destroys itself