Let $R$ be a commutative ring.  Then, is it possible to extend this to have a unity?  That is, is there a commutative ring with unity $R'$ such that $R$ is a subring of $R'$?
Let $R$ be an rng. (There may be no unity)  Then, does there always exist a ring(with unity) $A$ such that $R$ is a subrng of $A$?
TSA requirements regarding ID If the name on my boarding pass lists Debbie and my Drivers License lists Debra, will this be a problem? How to change the output redirection of a running process? I know how to redirect output and how to  in bash. Now, suppose I accidentally forgot to append the output redirection part to the command (e.g. 2&gt;&amp;1 or &gt; /tmp/mystdout) and my background process is already running for a while, can I still change to where stdout and stderr are being written to? I really would like not to kill and restart the application.  To be more specific as asked by  in his comment, I would like to fiddle with it in these scenarios in specific:   wrong output file forgot to redirect stderr to stdout   or a combination of both  E.g. I have Apache running and I can see the file descriptors:  /proc/8019/fd/0 -&gt; /dev/null /proc/8019/fd/1 -&gt; /dev/null /proc/8019/fd/2 -&gt; /var/log/apache2/error.log How to get a list of applications installed in Ubuntu dash? Is there a noun that doesn't have a plural in any of its forms? While attempting to answer  @ProgramFox has been trying to come up with an example of a noun with no plural.   The best I've come up with is egotism and Judaism.  ()  Some of the contenders I've already shot down are air, water, and money.  (Airs, waters, and monies are all legitimate plurals.)  My question is, a) Do my two examples have actual plurals?  b) Are there any other non-ism nouns that don't have a plural? Points disappear when zooming past certain scale in ArcMap? My points are disappearing when I zoom in past 300,000 in ArcMap.  I tried to repair geometry, but it doesn't fix anything?    I also checked the scale extents and those are turned off.  I can export the points to a new shapefile/feature class, but I'd like to not have to do that.    I'm using 10.1 on Windows 7 x64. Selection by attribute string with wildcard as part of name in ArcGIS Desktop? I have an attribute field in my file geodatabase (GDB) where I'm trying to select all records that contain an underbar in the string field.  The issue is that the underbar is considered a SQL wildcard on its own.  To illustrate: I need all data similar to "ID" = '42W_42_42E' or "ID" = '31A_31'  Using "ID" LIKE '%_%' returns all records, which isn't helpful.  The perfect solution would simply return a count on the number of records with the underbar in their ID attribute. Is losing privileges after placing bounty OK? My rep went over 2,000 today which meant I could edit other people's posts. Great! Then I added a bounty to a previous question, which brought me back down to 1,984...and I can no longer edit other posts. Should this changed? Or is this ideal? Passing an array as a function parameter in JavaScript Truncated trivariate normal - conditional expectation How can you find out which process is listening on a TCP or UDP port on Windows? Supersymmetry in Quantum Field Theory What new capabilities do user-defined literals add to C++? How do I brew an X potion? How can I get admin access to a Mac without knowing the current password? My Father died last year and I inherited his Mac Mini. My wife has retired and we are trying to set up the mini for her use but the changes we want to make require admin access and we do not have the information my father used to set up the machine.  Is it possible to reset the admin information without having the old information? If so, how would I go about it?   I am not a Mac user usually so any guidance will have to be pretty simple! Prevent Serialization of Base Class How long would a 150 Farad Capacitor light up an LED I have a bright white LED from a flashlight. Aproximatley How long will it light up with a 150 farad 2.5 volt capacitor. Do I need a resistor? And if so how many Ω? The capacitor is a maxwell 150 farad 2.7 volt boostcap . How exactly does lighting affect combat? I understand that there are different types of lighting (dim, bright, complete darkness), but I haven't been able to find anywhere in the DMH or PHB that specifically describes how these different types of light sources affect combat.   What impact does complete darkness have on players being able to see the locations of the monsters in the room? What impact does complete darkness have on combat rolls against monsters? Could anyone point me to a book/page that contains some more detailed information on this?   Thanks! How do I change the GRUB boot order? I have both Windows 7 and Ubuntu installed on a shared machine. Because a lot of the non-developers use Windows, I'd like to change the boot order to make it easier for them.  Currently the boot order looks like the following:   Ubuntu 11.10 kernelgeneric *86 Ubuntu 11.10 kernelgeneric *86 (safe boot)  Memory test Memory test Windows 7 on /dev/sda6   How do I change the default order so that Windows 7 is at the top of the list?   Windows 7 on /dev/sda6 Ubuntu 11.10 kernelgeneric *86 Ubuntu 11.10 kernelgeneric *86 (safe boot)  Memory test Memory test How do we perform transverse measurements in a two level system? In quantum mechanics any two level system can be mapped onto effective spin variables. If the system is defined by two energy levels, $|E_1\rangle$ and $|E_2\rangle$, the Hamiltonian is  $$ H = \left(\begin{array}{cc} E_1 &amp; 0 \\ 0 &amp; E_2 \end{array}\right) \, .$$  This can be recast as  $$ H = \frac{E_1+E_2}{2} 1\!\!1 + \frac{E_1-E_2}{2} \sigma_3\, .$$  $1\!\!1$ is the identity operator and $\sigma_3$ is the third pauli matrix. This is very nice because we can now apply our knowledge and intuition of spin dynamics to any two level system.  My question is the following: for a real spin I can measure expectation values of $\sigma_{1,2}$ by physically rotating my system and align its $x$ or $y$ axis with my measuring apparatus. How do I do this (in the lab!) with a pseudo-spin system? Imagine I am looking at a cold atom and I want to know if the system is in an symmetric or anti-symmetric superposition of $|E_1\rangle$ and $|E_2\rangle$, how do I do it? List of Ubuntu Versions with Corresponding Linux Kernel Version