I retired several P4 3.4Ghz PCs with 2GB RAM at the office. The hardware is still working but 4-5 years old. Which version of Ubuntu can I use to make these PCs useful. Never used Ubuntu before.
For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements?
Primary ideals in Noetherian rings For an $R$-module $M$ I have the following definition for a submodule $N\subset M$ to be $\mathfrak{p}$-primary: this is the case when $\text{Ass}(M/N) = \{\mathfrak{p}\}$, that is, $M/N$ is coprimary or $(0)$ is a primary submodule.  Now for an ideal $\mathfrak{q} \subset R$ this definition gives that $\mathfrak{q}$ is $\mathfrak{p}$-primary iff $\text{Ass}(R/\mathfrak{q}) = \{\mathfrak{p}\}$. It can be shown that this is equivalent with $\mathfrak{p}^n \subset \mathfrak{q}$ for some $n\in \mathbb{N}$ and the condition \begin{align*} \forall r,s \in R: rs \in \mathfrak{q}, r\not\in \mathfrak{p}\Rightarrow s \in \mathfrak{q}. \end{align*}     Now I suspect that if $R$ is Noetherian, and if $\mathfrak{q}$ is $\mathfrak{p}$-primary, then we have $\sqrt{\mathfrak{q}} = \mathfrak{p}$. I have shown this for PID's, but does this generaly hold?    And if so, is every ideal $\mathfrak{q}\subset R$ then $\sqrt{\mathfrak{q}}$-primary?   Many thanks. LaTeX templates for writing a thesis Aside from CTAN, what are good resources/repositories for Latex templates? In particular, I'm looking for some pretty Thesis templates (I'm familiar with classicthesis) How to remove the "Could not connect to the iTunes store" error message when your network does not allow access to the iTunes Store How do I deal with a runaway bride? Sometimes you just want to let out some steam, and troll about some technology or software. You are not looking for any answers, but for users with similar experiences and interesting stories. So why not create a separate discussion site (trolling.stackoverflow.com?), where you could ask questions like "why do you hate technology X" or "What are the stupidest bugs you encountered in X"? function $f(x)=x^{-(1/3)}$ , please check whether my solution is correct? Let $f(x)=x^{-(1/3)}$ and $A$ denote the area of region bounded by $f(x)$ and the X-axis, when $x$ varies from -1 to 1. Which of the following statements is/are TRUE?   f is continuous in [-1, 1] f is not bounded in [-1, 1] A is nonzero and finite     I try to explain :    graph is  :     False , since left limit is not equivalent to right limit. True , since  f(x) rises to $infinite$ at $x=0$. True , since we can calculate it by doing integrating the function Is it possible to simulate key press events programmatically in JavaScript? alias multi commands as one alias I made an alias for youtube-dl  with some options  like that  yd="youtube-dl -cit -f 18"   so I can download it like   yd URL   I want to modify it to show only the two lines from the output using   grep -e "Downloading video #" -e ETA  I can make it in two aliases using the |   but is there a way to make it one alias How can I rename many files at once? In Java, how do I call a base class's method from the overriding method in a derived class? What is the relationship between redshift and conformal time ?   For example in a paper i found:   taking $z_e = 3234 $ at the time of radiaton-matter equality yields the conformal time $\frac{\eta_e}{\eta_0} = 0.007$ and taking $z_E=0.39$ at matter-$\Lambda$ equality yields $\frac{\eta_E}{\eta_0}=0.894$ and setting redshift at decoupling $z_d=1089$ yields $\frac{\eta_d}{\eta_0} = 0.0195$  where $\eta_0$ is the present decoupling time.  Further some cosmological parameters are given as :  $\Omega_r = 8.36 \times 10^{-5}, \Omega_m = \Omega_b + \Omega_{dm} = 0.044 +0.226, \Omega_\Lambda = 0.73,  H_0=0.72$  Now how can i calculate all those $\eta_e, \eta_E, \eta_d, \eta_0$ from given redshift values and/or above parameters ? I searched whole of my text books trying to find an explicit relation for conformal time $\eta$ but all i got was $ \mathrm{d}t=a(t)\mathrm{d}\eta$. Any help would be very helpful. How to find out the terminal command of an application? Java logical operator short-circuiting A cyclic group is a group that is generated by a single element.  That means that there exists an element $g$, say, such that every other element of the group can be written as a power of $g$.  This element $g$ is the generator of the group.  Is that a correct explanation for what a cyclic group and a generator are? How can we find the generator of a cyclic group and how can we say how many generators should there be? Would you please tell me which of the following terms is correct? If both are correct, are they equal?     I have no [...] I don't have any [...] Can I find out which tags I have created? This would be interesting to know.  The tags could be highlighted on the users page for example. ShareLaTeX compilation flags Is it possible and if so how can you pass flags to the ShareLaTeX compiler which one would have passed as parameters to the LaTeX compiler?  I am using the minted package and need to pass the -shell-escape flag. I have Ubuntu budgie 17.04 (budgie-desktop 10.2.9). While pressing Alt+Tab to switch between the windows, the windows are switched randomly and I am not able to select which window to shift.  This feature was available in Ubuntu 16.04 but not in Ubuntu-budgie-17.04.    How to resolve this? Answer turned to CW, votes pre-CW era doesn't count in tag specific stat My understanding is that if an answer becomes CW (one way or another), original author gets to keep the votes pre-CW.  Does this also keep the pre-CW vote count for the tag-specific stat? It doesn't look like it, because I checked recently and suddenly my number dropped. It looks like the tag-specific stat just counts votes for non-CW answers, and doesn't "discriminate" between the pre-CW and post-CW era. If it's eventually CW, then it simply contributes 0 votes.  I'm fine with the fact that my answer became CW (in this case, through the question having 30+ answers), but I would like to keep the votes I earned before it did for the tag stat.  Otherwise I think the system is "broken". Someone can go posting 30+ answers to questions where Jon Skeet answered, and all of Jon Skeet's answers would become CW, and he'd then be 0 at all tags. How many 6-letter permutations can be formed using only the letters of the word, MISSISSIPPI? I understand the trivial case where there are no repeating letters in the word (for arranging smaller words) but I stumble when this isn't satisfied. I'm wondering if there's a simpler way to computing all the possible permutations, as an alternative to manually calculating all the possible 6-letter combinations and summing the corresponding permutations of each. In addition, is there a method to generalize the result based on any P number of letters in a set with repeating letters, to calculate the number of n-letter permutations?  Sorry if this question (or similar) has been asked before, but if it has, please link me to the relevant page. I also apologize if the explanation is unclear, or if I've incorrectly used any terminology (I'm only a high-school student.) If so, please comment. :-)