I tried to show that there is no commutative ring with the unit whose group of units is isomorphic to $\mathbb{Z}/p^2\mathbb{Z}$. I can show if the ring is a finite field,it is easy. But I can no idea about general case. Please give me some advice.
Motivated by :   Which finite groups are the group of units of some ring? Which finite groups are the group of units of some finite ring? Which finite abelian groups are the group of units of some commutative ring? Which finite abelian groups are the group of units of some finite commutative ring?   It  that even for fields this is not simple to answer.  I expect the general question (Which groups are the group of units of some ring?, with no finiteness hypotheses) is even harder.
Using ArcPy to get all database names within server? I am trying to populate a folder with ArcSDE database connection files for all the databases within a server instance.  I need to be able to do this for several of our servers.  Although I know within SQL Server how to get a list of DB names from the sys.databases table, using the arcpy function CreateDatabaseConnection I cannot specify "sys" or "master" to make the connection.  Therefore, I need to know the name of a database currently in the server.  I am not sure how to make the check without hard-coding a name.  import arcpy arcpy.env.overwriteOutput = True  #Input the location where the database connection files will be stored connectionLocation = "F:/FolderName"  #Get the list of servers arcpy.CreateDatabaseConnection_management(out_folder_path= arcpy.env.scratchFolder,out_name= "GIS_USERCONFIG" ,database_platform="SQL_SERVER",\                                           instance = "XXXXXXX" ,account_authentication="DATABASE_AUTH",username="user",password="password",\                                           save_user_pass="SAVE_USERNAME",database= "GIS_USERCONFIG",schema="#",version_type="TRANSACTIONAL",version="dbo.DEFAULT",date="#") sdeConn = arcpy.ArcSDESQLExecute(arcpy.env.scratchFolder + "/GIS_USERCONFIG.sde") serverListSQL = sdeConn.execute("Select name from userservers") serverList = [] for i in range(0,len(serverListSQL)):     serverList.append(serverListSQL[i][0])  #Make a folder for each server instance and build the connection files for all DBs in the server instance for server in serverList:     folder = connectionLocation + "/" + server     if arcpy.Exists(folder):         print server + " folder already created"     else:         try:             arcpy.CreateFolder_management(connectionLocation, server)             print "Created Folder " + server         except:             print "failed to create folder " + server      #     arcpy.CreateDatabaseConnection_management(out_folder_path= arcpy.env.scratchFolder,out_name= server ,database_platform="SQL_SERVER",\                                           instance = server ,account_authentication="OPERATING_SYSTEM_AUTH",\                                           database= "master",schema="#",version_type="TRANSACTIONAL",version="dbo.DEFAULT",date="#")     sdeConn = arcpy.ArcSDESQLExecute(arcpy.env.scratchFolder + "/" + server + ".sde")     dbListSQL = sdeConn.execute("Select name from sys.databases")     dbList = []     for i in range(0,len(serverListSQL)):         dbList.append(dbListSQL[i][0])     for db in dbList:         arcpy.CreateDatabaseConnection_management(out_folder_path= folder ,out_name= db,database_platform="SQL_SERVER",\                                           instance = server ,account_authentication="OPERATING_SYSTEM_AUTH",\                                           database= db,schema="#",version_type="TRANSACTIONAL",version="dbo.DEFAULT",date="#")   Basically my issue is with the 2nd call for the function "CreateDatabaseConnection_management" since it needs a database that exists in the database (and I could not use "master or sys").  If you open this as a tool in arcmap, the input is a drop-down box that populates choices based on the databases in the chosen server instance.  Is there a way to do this in the code? Why can't I import a file in the init.m file? What are the limits of the Room of Requirement? How to select lines between two marker patterns which may occur multiple times with awk/sed Create Trigger that updates the same table before (or after ??) the Insert I have just started using triggers and one thing that I would need to do is to create a trigger that updates the same table that's inserting the row.  TABLE:  CREATE TABLE `city` (   `city_id` smallint(5) unsigned NOT NULL AUTO_INCREMENT,   `city` varchar(50) NOT NULL,   `country_id` smallint(5) unsigned DEFAULT '0',   `country` varchar(150) DEFAULT NULL,   `last_update` timestamp NOT NULL DEFAULT CURRENT_TIMESTAMP ON UPDATE CURRENT_TIMESTAMP,   PRIMARY KEY (`city_id`),   KEY `idx_fk_country_id` (`country_id`),   CONSTRAINT `city_ibfk_1` FOREIGN KEY (`country_id`) REFERENCES `country` (`country_id`) ON UPDATE CASCADE ) ENGINE=InnoDB AUTO_INCREMENT=6009 DEFAULT CHARSET=utf8;   Trigger:  DELIMITER $$ CREATE TRIGGER `populate_country_id` BEFORE INSERT ON `city` FOR EACH ROW BEGIN  IF NEW.country_id = 0  THEN     UPDATE city     INNER JOIN country B ON city.country = B.country     SET NEW.country_id = B.country_id;  END IF;  END $$ DELIMITER ;   MySQL is just returning: Can't update table 'city' in stored function/trigger because it is already used by statement which invoked this stored function/trigger.  Is there any way I can make this work?  Thanks everyone! How to connect two Dell P2415Q 4k displays to MacBook Pro 2016 What's the best way of connecting two Dell P2415Q 4k displays to the MacBook Pro 2016 with TouchBar and TouchID?  I have the monitors connected to an older MacBook Pro currently with two mini-DisplayPort cables. Can I somehow reuse those cables or do I need new ones?  Apple's support page  lets me know that:  "Note that although it uses a Mini DisplayPort connector, the Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter doesn't support connections to Mini DisplayPort displays."  So I guess reusing the cables is not the way to go? I just bought all the ingredients to make a soup in the crock pot. I was planning on having it cook all day, but I just realized the recipe only calls for it to cook on low for 3-4 hours. If I cook it on low for 3-4 hours, and then put it on warm before I leave for work, will it be a bacteria minefield or will it be warm enough to keep the food safe from bacteria? Partial SSL in rails How do I disable fog on specific camera/s How do you convert LPCWSTR to const char *? How does a battery ( primary cell ) work? I'm having an hard time understanding primary cells. There are plenty of videos and explanations about the reactions that happen inside the battery, but you must have a strong background in chemistry to really understand them. Instead, I would love to have a description that abstracts from the chemicals details, and still manages to explain its basic working princeples! I would like it to address the following questions/doubts:     Electrons flow form higher potential to lower potential so, when you buy a  battery, is an electric field already there, before connecting it to a wire? (I presume yes) So,How is this field created? Are the electrons at the top and the protons at  the bottom, or just electrons at the top and the bottom is neutral? How are electrons kept together in the same place before connecting the battery  to the wire? What does prevent them to flow inside the battery? How does the battery pump up the electrons? and at which rate? What makes it burn out? and after many cycles does it burn out?       I know there are a lot of questions but my mind is exploding. I don't expect everything to be abstracted from the chemicals but as long as you can through analogies, or intuitive principles, i'd love that. Anyway the main intent of the answer must be addressing the doubts listed. I am trying to prove:     $a\mid b \land b\mid c \Rightarrow a\mid c $   $a\mid b$ means that a divides b if there is an integer k, that $b=k\cdot a$  Please give me a hint on how to start, because I have no idea. When I upgrade from one version of Ubuntu to the next, the upgrade tool rightly disables all my PPAs, so that software compiled for or otherwise tied to the old version of Ubuntu does not interfere with the new version that I just upgraded to.  Is there any way to automatically re-enable and update any PPAs that provide packages for the new version of Ubuntu? For example, suppose I'm currently running Maverick, and I have two PPAs enabled, "foo" and "bar". Suppose that "foo" provides packages for both Maverick and Natty, while "bar" provides packages for Natty only. Is there a tool I could run after updating to Natty that would re-enable my "foo" PPA and update it to point to the Natty packages, while leaving the "bar" PPA disabled? I'm trying to make a command that creates a book that has many items with enchantments at level 1,000. However, I don't know why it keeps saying:     Data tag parsing failed: Unbalanced quotation:   {ench:[{id:0,lvl:1000}],Unbreakable:1,display:{Name:"Prot   It's supposed to say "Protection Armor", but it only shows "Prot" for some reason. This is the same with all of my other items. Here is the one part of the command that I've showed you:  {ench:[{id:0,lvl:1000}],Unbreakable:1,display:{Name:"Protection Armor"}} I have always recommended pressing ALT+F2 and typing for example gksu nautilus or gksudo nautilus both are equivalent; to run graphical programs with root privileges.  However, I have just installed raring on a test system and this no longer works.  gksu and gksudo are not installed as part of a default raring install; though they are in the repositories. In 12.04 at least gksudo was just a symbolic link to gksu  The reasons I have always done this are because while it is often safe to use sudo under some circumstances it can cause problems with graphical applications because gksu has you running the program as root while with sudo you are running as yourself but with elevated privileges.  This can mean you inadvertently change the owner of critical system files.  This can cause problems.  This reasoning is explained better here:         Why was command removed from a fresh install and what should we be using instead? Find all integers  $a$,$b$ and $c$ that satisfy the following equations  $a^2=bc+1\tag{i}$  $b^2=ac+1\tag{ii}$    I tried solving came out with following results:  $(i)-(ii)$ gives $a+b+c=0$ which implies, $a^3+b^3+c^3=3abc$  Multiplying equation $(i)$ with $a$ and multiplying equation $(ii)$ with $b$ and then subtracting $(i)-(ii)$ we get  $a^2+b^2+ab=1$ which can be written as  $(a+b)^2-ab=1$ , which can be further written as $c^2-ab=1$. I have been wondering what a gold piece is worth, due to the fact there are many things that cost the same, but in reality, are probably worth radically different prices, such as a Goat and a Whip, which both cost 1 gp.  What is a gold piece really supposed to be worth? Like, how would things be priced if they were in familiar modern monetary units instead of "gp"? That would give me something to base my adjustments to abnormal prices on, such as items not listed in the PHB. Einstein equation  where $E$ is energy, $m$ mass, and $c$ the speed of light in vacuum. So does it mean objects without any mass does not posses energy for eg lights photons does not have mass but how can they posses energy How to layout irregular paragraph shape I have found this in the cover of seminar(one tool to make slide) document.  The final result I have captured below:    The complete document can download .  I wonder how to make this. Is there any easy way? I was using Windows XP, I like Ubuntu, but I'm wondering,because as  I'm a professional photographer &amp; photo editor.  I do my work with Photoshop, so will photoshop work in ubuntu?