Should I be mentioning people in separate comments or a unified comment?
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If I roll two fair dice, the probability that I would get at least one 6 would be.... Perfect infinitive How to mount a VirtualBox shared folder at startup? How put color in all math mode? Irreducible Components of the Prime Spectrum of a Quotient Ring and Primary Decomposition If $L_i/K$ are Galois extensions of number fields, $i=1,\ldots,n$, and $L=L_1\cdots L_n$ is the compositum. Then it's true that a prime $\mathfrak{p}$ of $K$ splits in $L$ if and only if it splits in all of $L_i$. Does this also hold if the $L_i$ are not Galois extensions of $K$?  The proof that I know regarding the compositum uses the fact that the $L_i/K$ are Galois, so is this true in the more general setting and how would one prove it? Show that $R/I\otimes_R R/J\cong R/(I+J)$ Let $R$ be a commutative ring with identity and $I$ and $J$ be ideals in $R$.     Show that $R/I\otimes_R R/J\cong R/(I+J)$ as $R$-modules.   This is what I tried.  Define a map $f:R/I\times R/J\to R/(I+J)$ as $f(\bar r, \bar s)=rs+(I+J)$. This is a well-defined bilinear map.  By the universal property of tensor products, we get an $R$-linear map $F:R/I\otimes_R R/J\to R/(I+J)$ which sends $\bar r\otimes \bar s$ to $rs+(I+J)$.  This map is surjective.  So all we need to show is that the kernel of $F$ is $0$.  But I am unable to do this. Interaction term positive while components are negative? I am confused about the interpretation of my interaction term , I have been through similar questions but I am still not sure about the interpretation that I should give to my output .  So this is my model , Y  stands for earnings management , X1 = CSR , X2=CEO duality , as you can see both of the coefficients are negative CSR reduces earnings management manipulation and Duality in my sample reduces em as well  which is in line with the literature and confirm my hypothesis , but to my surprise my interaction term is positive and significant does that mean that CSR combined with duality increase EM ? Or that CEO duality moderates the effect of CSR on EM knowing that in papers that I've read, they only use&quot; moderate &quot;when the interaction term and the components are all negative . Could you please help me ? I am supposed to comment my results but I don&quot;t understand this . Thank you Is Site Traffic Data Gone for Good After Fixing Previous Bug? There was a previous bug affecting site traffic statistics showing -zero- for months (). This has been fixed in that it is now graphing the data.  It appears that previous data may be lost? The graphs below are from . I don't have access to any other sites' graphs to see if they are showing similar results. When should we use proximity rule in "either/or", and "neither/nor"? According to this , if at least one of the nouns involved is plural then it should take the plural form of the verb. Otherwise, it should take the singular form of the verb. But in the last part it says not all grammars agree to those rules thus proximity rule applies. However, it doesn't explain when to apply the proximity rule and when not to use the former rules. In Windows, one can create a new file using Right Click -> Add New -> Type of File. Is there an analogous action in Lion?  I just want to create a new blank file on my Desktop. How to round a number to n decimal places in Java What I would like is a method to convert a double to a string which rounds using the half-up method - i.e. if the decimal to be rounded is 5, it always rounds up to the next number. This is the standard method of rounding most people expect in most situations.  I also would like only significant digits to be displayed - i.e. there should not be any trailing zeroes.  I know one method of doing this is to use the String.format method:  String.format("%.5g%n", 0.912385);   returns:  0.91239   which is great, however it always displays numbers with 5 decimal places even if they are not significant:   String.format("%.5g%n", 0.912300);   returns:  0.91230   Another method is to use the DecimalFormatter:  DecimalFormat df = new DecimalFormat("#.#####"); df.format(0.912385);   returns:  0.91238   However as you can see this uses half-even rounding. That is it will round down if the previous digit is even. What I'd like is this:  0.912385 -&gt; 0.91239 0.912300 -&gt; 0.9123   What is the best way to achieve this in Java? In what sense are Asgardians "immortal" in the MCU? I'm looking to get that from a graph. but problem is that graph is in image form. Now I want to extract data in excel from that graph. how can i do it? I'm using office 2003. How do I load an mp4 video with multiple audio tracks into blender? Getting "'file' is different from the same file on the system" when I attempt to update through synaptic "Mixed declaration and code" warning, is it worth addressing? Why do diamonds shine? Can a java file have more than one class? 'find' utility does not output all files when using wildcards Running:  $find . -name *.exe   gives:  ./MakeItSo_1.2.2/MakeItSo_1.2.2/MakeItSo.exe ./MakeItSo.exe   but those are not the only exe files in the directory. For example, running  $find . -name ATLTester.exe   gives:  ./Debug/ATLDmoVexaTester.exe