Complement of a prime ideal is a subset closed under multiplication, containing 1
Is the complement of a prime ideal closed under both addition and multiplication?
Multiple "order by" in LINQ I have two tables, movies and categories, and I get an ordered list by categoryID first and then by Name.  The movie table has three columns ID, Name and CategoryID. The category table has two columns ID and Name.  I tried something like the following, but it didn't work.  var movies = _db.Movies.OrderBy( m =&gt; { m.CategoryID, m.Name }) What's the most popular way to encrypt individual files or folders? "Error: Invalid signature" when configuring dual boot Ubuntu 14.04 and Windows 10 Is there a gender-neutral pronoun that can replace “his” or “her”? What is the difference between 'su -' , 'sudo bash' and 'sudo sh'? I would like to know what is the difference between    su - sudo bash sudo sh   I cannot login as root while doing su - because I do not have the root password - I mean I have my user password with which I can sudo "command"  but this password does not work for su - I can log in as root with sudo bash with my user password and I can login while doing sudo sh but then I get a command prompt in this form # How to hide a(n) (NTFS) partition from ubuntu I need to hide an NTFS partition from listing in the nautilus. How can I achieve that?   Is there any tool to do that?   And how can I hide files in ubuntu (except . operator) Does the Symmetric difference operator define a group on the powerset of a set? $G$ is the set of all subsets of a set $A$, under the operation of $\triangle\;$: Symmetric Difference of sets.  $A$ has at least two different elements.  I need to check if this is a group, and if it does to show if the group is abelian and/or finite.  Associativity - easy from Symmetric Difference. Identity element - empty group. Inverse element - each element is inverse to itself. Am I right?  abelian? finite? I remember seeing an upper bound for the binomial $\binom{n}{k}$ with an exponential function, something like $\binom{n}{k}\leq \left(ne/k\right)^k$. What exactly is it, and are there other similar good upper bounds for $\binom{n}{k}$?  Edit: As the link in Macavity's comment shows, the bound is indeed $\binom{n}{k}\leq \left(ne/k\right)^k$. How can we prove this? What is meant by a continuous-time white noise process? Benchmarking hosting providers IO with Bonnie After mis-reading this question:  I found myself wondering if there are other non-weapon items such as tools that utilize lightsaber technology.  Example: the lightsaber bread knife Can anyone help me with a solution? How long does it take for badges to be awarded? How are they generated? How to view recently opened media files? In windows we have an option to view recently opened media files as my recent documents, I was  wondering does there exists something like that in Ubuntu?  via terminal or via GUI? How to change the numbering of \part, \chapter, \section, ... to alphabetical, Roman numbers, etc Get most common value for each value of another column in SQL I have a table like this:   Column  | Type | Modifiers  ---------+------+-----------  country | text |   food_id | int  |   eaten   | date |    And for each country, I want to get the food that is eaten most often.  The best I can think of (I'm using postgres) is:  CREATE TEMP TABLE counts AS     SELECT country, food_id, count(*) as count FROM munch GROUP BY country, food_id;  CREATE TEMP TABLE max_counts AS     SELECT country, max(count) as max_count FROM counts GROUP BY country;  SELECT country, max(food_id) FROM counts     WHERE (country, count) IN (SELECT * from max_counts) GROUP BY country;   In that last statement, the GROUP BY and max() are needed to break ties, where two different foods have the same count.  This seems like a lot of work for something conceptually simple.  Is there a more straight forward way to do it? Use of "would" for subjunctive phrases This has been bugging me for some time; I tried to look for previous questions here but my language tools may not be sharp enough to phrase my query correctly so please forgive me if this has already been posted here.  Speakers of English as a foreign language tend to incorrectly use the word "would" when using some particular subjunctive constructs. Here is  (this time presumably by a native English speaker):     If that would happen, you won’t be alone.     (One correct version being "If that happens, you won't be alone".) I have detected this in speakers of a number of languages so I feel this is more likely to be a feature of the English language itself than a carry-over from their native language.  I have a faint intuition that this is because , and it certainly doesn't help that , but I can neither make that precise nor even really phrase a concrete question. Can someone shed some light on this?    Edit: just to provide some real-world examples of what I mean, here is one example taken from :     Publish or Perish is designed to empower individual academics to present their case for research impact to its best advantage. We would be concerned if it would be used for academic staff evaluation purposes in a mechanistic way.   This is obviously ungrammatical (to me), but I'm not sure how to characterize the mistake, or what the likely causes are (e.g. whether it follows from analogous constructions in other languages). How to change Function (Fn) Key behavior on wireless Logitech keyboard I do have a wireless Logitech K750 keyboard (silver Mac version) connected to a Lenovo ThinkPad (via the unifying USB receiver, together with a wireless Logitech mouse M705) and currently running Ubuntu 12.04.  By default the F-keys are mapped as multimedia/function keys, e.g. Play  /Pause. As I don't use them very often, I want the F-keys to behave like the "real" F-keys (F1-F12). How can I do that?  I know there is an option in the BIOS settings, but this only toggles the built-in keyboard of the notebook, not on my wireless keyboard.  I know there is a way to change this for the Apple wireless keyboard (), but there is no "parameters" directory in /sys/module/hid_logitech_dj/.  Any ideas? Or is there maybe a way to do this in a later Ubuntu version (13.04)?  UPDATE:  lsusb -d 046d: shows Bus 002 Device 005: ID 046d:c52b Logitech, Inc. Unifying Receiver  UPDATE 2: Thanks a lot for your help Lekensteyn. Finally  works just fine. In the "Known Issues" of Solaar it says that it does not work with the Nano Receiver. But I have one and it works just fine. Just don't forget to read the installation instructions and run the rules.d/install.sh script. It also recognized my M705 Mouse. I am thinking of moving my extensive eBook library to iBooks or Kindle. Has anyone done this, and what does it take?  I just don't want book libraries in multiple proprietary formats, and have to look for content across apps. Can I publish an article or thesis about my research without supervisor?