Field of Fractions over Formal Power Series
If $a_0\in R$ is a unit, then  $\sum_{k=0}^{\infty}a_k x^k$ is a unit in $R[[x]]$
In the sentence: "Drinking and driving IS dangerous", why does the verb "to be" need to be singular? In the sentence: "Drinking and driving is dangerous". Drinking and driving are both subjects and the word dangerous is the object (I think) but why do I have to use the verb to be in singular? I'm working under 12.04 and suppose I have a Firefox windows active (or in foreground) with English as input language and I need to type a document in other language using some text editor.   With the text editor in foreground (or active) and the input language set to a non-English one, when I bring Firefox in foreground (or making it active) the input language remains set to the non-English and the language flag does not switch to English (as it would be expected, since I do not alter the language during the whole Firefox session).  Because of this, I have to make extra moves and change the input language manually every time I switch from the text editor to Firefox and back to text editor. This was not happening with 10.04, and each application windows had the corresponding input language set to its default or previous session every time I was bringing it to the foreground!   How will I make 12.04 to behave the same way? DEF file syntax error in visual studio 2012 CSV for Excel, Including Both Leading Zeros and Commas Why do I get "Permission denied (publickey)" when trying to SSH from local Ubuntu to a Amazon EC2 server? I have an instance of an application running in the cloud on Amazon EC2 instance, and I need to connect it from my local Ubuntu. It works fine on one of local ubuntu and also laptop. I got message "Permission denied (publickey)" when trying to access SSH to EC2 on another local Ubuntu. It's so strange to me.  I'm thinking some sort of problems with security settings on the Amazon EC2 which has limited IPs access to one instance or certificate may need to regenerate.  Does anyone know a solution? I want to find questions within the C++ tag but with zero answers. How can I do that? Can we have some tools to handle link rot? There are many links posted in answers, and some in questions, that are either stale or broken.  An example is the change to  on-line documentation this year to do away with separate 'Optional' and 'Core' tasks areas in the documentation - the old links 404 now.  I've fixed a bunch of 'optionaltasks' broken links, but searching for 'coretasks' in Stack&nbsp;Overflow questions returns over 300 matches...  Are there any tools for us to review and fix these - with an emphasis on the fixing - without sifting through completely manually?  Is it time for some refactoring tools for Stack&nbsp;Overflow content, in particular, for links?  Also, I'd be interested to know if there is an analysis of links (as found in the Stack&nbsp;Overflow data dumps) out there. Answer: there is a  of a sample of links and images, but it's getting a bit out-of-date. On which Canary island is it possible to sleep on the beach? We are planning a two-night trip to the Canary Islands. The cheapest options include Lanzarote and Las Palmas for flights. Travel dates are last week of November, so I guess weather should be okay. I have never been to these islands. I'd like to sleep on the beach in a tent or mattresses. Is that possible, safety, legality, and weather? It would also be nice to know how populated with tourists the islands are. C# List Sort by x then y Similar to , we want to sort by one element, then another.  we want to achieve the functional equivalent of   SELECT * from Table ORDER BY x, y     We have a class that contains a number of sorting functions, and we have no issues sorting by one element. For example:    public class MyClass {     public int x;     public int y; }    List&lt;MyClass&gt; MyList;  public void SortList() {     MyList.Sort( MySortingFunction ); }   And we have the following in the list:    Unsorted     Sorted(x)     Desired ---------    ---------    --------- ID   x  y    ID   x  y    ID   x  y [0]  0  1    [2]  0  2    [0]  0  1 [1]  1  1    [0]  0  1    [2]  0  2 [2]  0  2    [1]  1  1    [1]  1  1 [3]  1  2    [3]  1  2    [3]  1  2   Stable sort would be preferable, but not required. Solution that works for .Net 2.0 is welcome. Left and right subscript / superscript I am trying to put two subscripts at the left and right of a character. For example, something like:  _{t} p_{x}  where p is in the middle. How do you do this? Why can't I join a friend's world on Minecraft PE? I'm on my tablet playing Minecraft PE. My boyfriend rang me and asked me to join his Minecraft PE world. However, I can't do it because the game doesn't show his world. What's wrong and how can I fix it? How to disable "time travel" entirely? How can I download free apps without registering an Apple ID? "This Apple ID has not been yet been used before in the iTunes Store. Tap review to sign in, then review your account information."   I keep getting this message when I try to install free apps from App Store. I don't want to give my account info until I actually purchase something.   Can I not download free apps until I provide my account information? My email verification is complete. I'm using an iPhone 3GS logged in to my iTunes account. During graduate studies online application submission period, is there any preference given for an applicant if he/she submits his application at the beginning of that period compared with someone who submits his/her application couple of hours before the deadline?  Or as long as the applications are complete there is absolutely no difference! Is it possible to restore a MySql database only using files from Data directory? I have asked this question before  The first guy solved it in a way, but  i would like to know is there any efficient way to do so, because i did the same for N = 13 and N = 15  which took long time.  This problem is from a pen and paper test, ZIO-2018 Can i solve it with an efficient algorithm, well i am pretty beginner in algos, so if there is one kindly descibe it how can i do so?  Thank you What's the difference between the five masses: inertial mass, gravitational mass, rest mass, invariant mass and relativistic mass? How does pointing a CNAME on my domain to a service-provider's server enable them to offer customized services? Given Newton's third law, why are things capable of moving? Given Newton's third law, why is there motion at all? Should not all forces even themselves out, so nothing moves at all? When I push a table using my finger, the table applies the same force onto my finger like my finger does on the table just with an opposing direction, nothing happens except that I feel the opposing force. But why can I push a box on a table by applying force ($F=ma$) on one side, obviously outbalancing the force the box has on my finger and at the same time outbalancing the friction the box has on the table? I obviously have the greater mass and acceleration as for example the matchbox on the table and thusly I can move it, but shouldn't the third law prevent that from even happening? Shouldn't the matchbox just accommodate to said force and applying the same force to me in opposing direction? How can I trigger a command when a player is hit by a Snowball? I am trying to make a snowball that triggers a command when it hits a player in 1.15, but I don't know how to do that. When I do execute at @e[type=snowball] run gamemode spectator @a[distance=..2] it only runs the command if it goes right next to them.