A finite dimensional algebra over a field has only finitely many prime ideals and all of them are maximal
Artinian affine $K$-algebra
Why are some actors uncredited in certain films? Eli Wallach  in Mystic River. Olivia Williams  in X-Men: The Last Stand. However, neither of them (according to IMDb) is credited in the movie. These two instances are simply examples.  Why are some actors, who are oftentimes quite well known, not credited in certain features? How to find web hosting that meets my requirements? In response to  question, I started to think about what it means when a Wild Magic Surge results in a "You cast spell-X".  So, "specific beats general" gives:   You can cast a second spell when you would not normally be allowed to You can cast a spell you don't know If the surge forces you to cast a concentration spell you would lose any concentration spell that you currently had active Subject to what the specific entry says you can target it how you like Unless the specific entry prohibits it you could use metamagic on the spell   I am pretty confident in all of the above but if anyone disagrees please address in an answer.  Here comes the question.  How does this impact on your available spell slots?  "You cast ..." to me suggests that if you have an applicable slot available then you have to use it to cast the spell because that is the general rule for casting spells but if you don't then "specific beats general" and it is cast anyway.  Specific examples:     You cast fireball as a 3rd-level spell centered on   yourself   This must be a 3rd level spell:   if you have a 3rd level slot available you have to use it? if you don't, if you have 5 sorcery points and a bonus action available must you use these to get that slot? if you don't have any of that then the spell goes off anyway?      You cast confusion centered on yourself.   No level specified and confusion is a 4th level spell:   if you have a 4th level slot available you have to use it? if you have a 4th, a 6th and an 8th level slot you can choose which one to use? if you have only a 5th level slot but also 6 sorcery points and a bonus action, you could choose to use the 5th level slot or use the points to create a 4th level slot? if you don't have any 4th level or higher slots but you have 6 sorcery points and a bonus action available must you use these to get that slot? if you don't have any of that then the spell goes off anyway?   And so on ... I'm looking for one word which describes what a student who missed classes needs to do Shortcut to open Terminal and run some commands What is a primary decomposition of the ideal $I = \langle xy, x - yz \rangle$? Given the ring $k[x,y,z]$, where $k$ is a field, and an ideal $I=(xy,x-yz)$, find a primary decomposition of $I$.    I tried to draw the graph of the variety of $I$ and get a decomposition of $(x,y)\cap(x,z)$ (the two prime ideals corresponds to the irreducible components of the variety), but apparently these two ideals are not the primary decomposition of $I$, and I don't know how to fix this.  I would really appreciate it if someone can help me. thx \@seccntformat only for section What are irreducibles in the ring $R$ of entire functions? Here's how far I have gone:  I first find the units in $R$. Let $f$ $ \in $ $R$ be a unit. Then $\exists$ $g$ $\in$ $R$ such that $fg=1$, i.e $f(z)g(z)=1$ $\forall$ $z$ $\in$ $\Bbb C$.  Then, $f(z)$ $=$ $\frac 1{g(z)}$ $\forall$ $z \in \Bbb C$. Hence $f(z),g(z) \neq 0$ $\forall$  $z \in \Bbb C$.  Now to find the irreducibles, let $f \in R$ be an irreducible. Hence whenever  $f(z)=g(z)h(z)$ for $g,h \in R$, then $g$ or $h$ is a unit.  Let $h$ be the unit and $\alpha$ be a zero of $f$. Then $f(\alpha)=g(\alpha)h(\alpha)=0$ $\Rightarrow$ $g(\alpha)=0$. Hence $z-\alpha$ is a factor of $g$. So $g(z)=(z-\alpha)^ng_1(z)$ for some $n \in \Bbb N$, where $g_1$ is unit. Since $f$ is irreducible, hence $n=1$.  I'm stuck here. What can be my next step? I got a integrated GD, which is Intel, and another discrete GD, AMD Radeon 6490 HD I am using ubuntu 11.10  1st, when I boot into Windows, my GD is indeed AMD Radeon 6490 HD, but when I boot into Ubuntu, it shows that I have AMD Radeon 6470 instead.  2nd, I try most methods only to install driver for my AMD/ATI graphic card. First by jockey(fail, boot with unity 2D instead) and install manually (fail, boot into blank screen).   3rd, I give up using the AMD/ATI graphic card. Then I got a new problem. Both my graphic cards are powered on on startup, which causes my laptop to over heat.   I view the content of /sys/kernel/debug/vgaswitcheroo/switch  0:DIS: :Pwr:0000:01:00.0 1:IGD:+:Pwr:0000:00:02.0   Then I switch off IGD using echo OFF &gt; /sys/kernel/debug/vgaswitcheroo/switch and I get  0:DIS: :Off:0000:01:00.0 1:IGD:+:Pwr:0000:00:02.0   But after I reboot, the discrete graphic card is powered on again. How to solve this? Different ways to prove there are infinitely many primes? I have a common scenario in app design, where I need to store an ordered list, and make the ordering easily accessible and adjustable via an application UI.    The ordering operations are simple and operate on only one item at a time - move to top, move to bottom, move up one position, or down one position.  These positioning operations may be interspersed in with typical add / edit / delete list operations.  For discussion, this is a single-user app and db store.  Because the objects can be highly complex, I'd like to avoid caching the entire list client-side, and tracking newly created objects in memory until a big save operation occurs.    I am using MS-SQL almost exclusively on these projects, and I'm wondering if there are db features, SQL features, or design patterns I should be using to better support the management of ordered lists.    My current approach is to use a DECIMAL column to store the list positions, which become fractional during the item move process.  Then I sort the list and re-generate integer positions to normalize list.  Following this operation, it's ready for another item move.   In an example implementation, I create a column named Seq for position tracking.  Once decimal place is enough for the .5 storage.   [Seq] [decimal](10, 1) NOT NULL   When an item is re-positioned in the app UI,    I UPDATE that record with new Seq value I retrieve the full table, sorted ascending by Seq and regenerate all Seq values in the table from a 1-based integer series   The new Seq value is easily calculated-    Move to top = 0 Move to bottom = MAX(Seq) + 1 Move up = subtract 1.5 from the current Seq value Move down = add 1.5 to the current Seq value   As lists get longer, updates get slower, since I'm doing N UPDATE statements, where N is the number of rows in the table, so it seems only suitable for small tables.    Is there some kind of in-built capability for managing an ordered list in SQL or MS-SQL? Is there a means to update multiple rows in one call?    A far more performant approach would be to allow more decimal places, and then position at the median of the two adjacent items, with no re-sequencing on the list.     Move to top = Min(Seq) - 1 Move to bottom = MAX(Seq) + 1 Move up = median of the 2 previous item Seq values Move down = median of the 2 following item Seq values   This approach only requires one SELECT (containing 2 rows max) and one UPDATE.    However with enough re-positions I imagine the field would run out of decimal places. For example, if I start with items at positions 10 and 11, and keep moving items down the list from position 9, they'd be given sequences of 10.5, then 10.25, then 10.125.  After 10 moves, the positions get lengthy... 10.0009765625.    UPDATE #1 - IMPROVED RE-SEQUENCING OF THE LIST  Regarding re-sequencing, I'm more caught up on row_number(), OVER, and WITH capabilities in MS-SQL.  It's nice to find that there's a much smoother way to re-sequence the list in a single UPDATE operation;  with OrderedItems as  (     select         ItemID,         Seq,         row_number() over (order by Seq asc) NewSeq     from          Items ) update OrderedItems set Seq = NewSeq When is it appropriate to end a question without a question mark? F# insert/remove item from list I am using an old laptop and doing heavy processing that needs high CPU usage for a long time (~30mins - 2hours). When the process puts heavy load on CPU for a long time, CPU overheats and computer shuts down. I don't want to use a cooler/stand because I am carrying this laptop around and working outside home.  Is there a way/application that I can limit CPU usage of a process in Windows?  Note: Setting the priority of the process from task manager does not work.  Note 2: Fans are clean. I have been playing with the settings for the text object recently, and every time I add a new text object, I need to change the font to my favorite one. (Eurostile LT ExtendedTwo) Is there any way to change the default font so I do not need to change it every time I add a new text object?   Example: Cancellation Law for Direct Sums - What is wrong with this argument? My question is, if you create a new domain user account for each of the SQL Server processes, what permissions should be set for each account? Or does the SQL configuration manager actually take care of this, and I just had an unforeseen issue?  I quite often have to setup Microsoft SQL Server and wondered if anyone can provide advice on configuring the accounts the services should run as. IMO this has been vaguely documented by Microsoft, while they point you in the right direction I have never been able to find any concrete examples.  To summarize what I've seen so far:  For simple deployments\development environments it is OK to use the virtual account defaults the installer uses: e.g. NT SERVICE\MSSQLSERVER  Avoid using the SYSTEM account, this is not secure.  For production and in domain environments it's recommended to use either a Managed Service Account, or create a domain user account (not an admin) for each service. Allegedly if you use a domain account at installation time the installer will set any required permissions for you.  If changing the service account on an existing install from a virtual account to a domain account the recommendation is to use the SQL Server configuration manager to set the new service accounts. Allegedly this will set any required permissions for you.  I just tried changing the service account in an existing install to a domain account and it would give me a logon failure until I granted the account log on as service permission, which contradicts the part where the SQL Server configuration manager will set any required permissions. (Although I'm not sure if a GPO may have interfered with setting this local security policy)  Microsoft does provide a list of the permissions that the SQL Server Setup grants .  But it's not clear to me if that is something I should be doing manually for the user I create to run the service as, or whether using the SQL config manager should automatically set these permissions.  SQL Server 2014, Domain Controller is on Windows Server 2008 R2. First, if you have a better suggestion for title I'm really opened to suggestions, but it is the best I came up with.  If I touch an electric line and the earth, I will get electrocuted.  However, if I touch the positive of a car battery, people told me the same thing won't happen...why is it?  It seems I need to touch the battery positive and the battery ground. Pacf lag axe , is not an integer I'm trying to use ARIMA process to predict the behaviour of a time series, the probleme I face is that I can't get the order of each component of ARIMA, the lag is between 0 and 1, same goes for the acf. The time series has no tendency, and I guess no seasonality.     My question is : Does this mean that ARIMA orders are all 0s, and if so, is the HoltWinters a good (or the best) solution for modelling this kind of TS ? Hello,  I'm getting this error every time when I boot my computer. My Ubuntu installation is fresh and I was got a few error on last step while install Ubuntu (because i have problem with my CDROM driver). Anyway, installation is continued .   For example when i tried to open ADDITIONAL DRIVER and LANGUAGE SUPPORT (on System Settings) nothing happened, it's not opening.  When i try this in terminal gnome-language-selector i'm getting this error  Traceback (most recent call last):   File "/usr/bin/gnome-language-selector", line 8, in &lt;module&gt;     from LanguageSelector.gtk.GtkLanguageSelector import GtkLanguageSelector   File "/usr/lib/python2.7/dist-packages/LanguageSelector/gtk/GtkLanguageSelector.py", line 34, in &lt;module&gt;     from aptdaemon.gtk3widgets import AptProgressDialog   File "/usr/lib/python2.7/dist-packages/aptdaemon/gtk3widgets.py", line 61, in &lt;module&gt;     class AptStatusIcon(Gtk.Image):   File "/usr/lib/python2.7/dist-packages/aptdaemon/gtk3widgets.py", line 66, in AptStatusIcon     def __init__(self, transaction=None, size=Gtk.IconSize.DIALOG): AttributeError: type object 'GtkIconSize' has no attribute 'DIALOG'   Also getting this error for jockey-gtk  Traceback (most recent call last):   File "/usr/bin/jockey-gtk", line 418, in &lt;module&gt;     sys.exit(u.run())   File "/usr/lib/python2.7/dist-packages/jockey/ui.py", line 461, in run     self.ui_show_main()   File "/usr/bin/jockey-gtk", line 81, in ui_show_main     col_icon.set_sizing(Gtk.TreeViewColumnSizing.AUTOSIZE) AttributeError: type object 'GtkTreeViewColumnSizing' has no attribute 'AUTOSIZE'   I'm worrying about are there any lack . I don't know what's wrong with my installation.  Are there any way, check my installation (packages, files etc..) .