If an integral domain $A$ is integrally closed, then so is $A[T]$
Trouble with proving $A$ is an integrally closed domain $\Rightarrow$ $A[t]$ is integrally closed domain
Are all multiplicative functions additive? I noticed that Synonymizer is only a bronze badge. Yet in order to obtain this badge you need to have 2500 reputation or more to even create tag synonyms. Then, on top of that you also need to be able to find a tag synonym.  Only 514 of these have been awarded... This makes the BRONZE badge Synonymizer rarer to have than most the gold medal badges. So my question is, why is this a bronze badge? The question is as follows.  Imagine we have two closed geodesics on a surface, where these two geodesics bound a cylinder together and the geodesics are diffeomorphic to circles.  Can the cylinder have $K&gt;0$ everywhere or $K&lt;0$ everywhere?  Here $K$ is Gaussian Curvature.   What's confusing me about this question is that a cylinder has Gaussian Curvature of $K=0$ everywhere, so wouldn't the answer to both questions be no?  But then I don't get the point of the question with the geodesics.  Thank you in advance Why do we need to discard one dummy variable? I have learned that, for creating a regression model, we have to take care of categorical variables by converting them into dummy variables. As an example, if, in our data set, there is a variable like location:   Location  ---------- Californian NY Florida   We have to convert them like:  1  0  0 0  1  0 0  0  1   However, it was suggested that we have to discard one dummy variable, no matter how many dummy variables are there.   Why do we need to discard one dummy variable? Converting ArcGIS layer style to Styled Layer Descriptor (SLD) file? I am putting together a GIS server using GeoServer and need some help with importing my layer styles from ArcGIS 10 to  format.    I have one layer in ArcMap properly symbolized and labeled, how can I get this layers symbolization and labeling into a SLD file? Draw power from a portable mobile charger to power circuits I usually power my beginner prototype circuits using mb102 power supply board, but it needs an external elimeter to draw power and then regulate it.  I was looking for a portable solution for my 5 volt and 3.3 volt circuit needs and came up with using a portable battery charger for mobile phones.  I tried powering up a simple transistor and LED circuit with it but it wouldn't power-up.   I feel that there is some load sensing circuit in the portable charger which doesn't detect these low power circuits.  I also tried connecting different resistors to the charger, the charger outputs 5 Volts for a few seconds and then again shuts down and doesn't stay ON continuously.  It would be really comfortable to use a portable charger since it could be charged using a phone charger and would be very handy.  What can I do to make the charger output power on low loads? Has the speed of light changed over time? Could someone judge my (stoner) hypothesis that the speed of light has changed over time -- i.e. as the universe has expanded in volume light has slowed down, perhaps going so far as back to the big bang when it was infinitely fast and there was no time because everything happened at once etc. Thinking that the speed at which information can propagate through the universe is linked to the size of it seems intuitive to me. My question -- is there an easy disproof of this? Would Einstein have to be wrong? Does it violate anything supposedly more fundamental such as quantum or string theories? Do any current experiments invalidate it? If not can you show me in any case why you think its unlikely.   Edit 8/24  I'm accepting Mark M.'s answer but will post this here because there is a character limit on comments  @Mark M thanks, good answer but as someone who has only read some popular physics, and should leave this to the experts, I'm still muddled in my personal theory. I don't see why you should need two units to measure the speed of light. The thing I have a hard time wrapping my head around is the relation of time and distance. They seem like they could fundamentally be the same thing. If you say time is measured fundamentally by the vibration of so and so quantum object in space... why can't we just measure that vibration distance as the constant... I'll repeat myself to try to be clear... there is a certain minimum distance that particles have to go to interact with each other... if it wasn't vibrating there wouldn't be time,its what creates the illusion of time...so instead of talking about speed or c as distance/time.... can't we simply talk about that distance a quantum object vibrates....I'll lead up to my point.....perhaps there can need be only one constant here, and that is the physical size of the universe. a tiny metal tuning fork doesn't appear to be vibrating at all but if you blew it up to the size of the empire state building the metal rods would move from window to window. perhaps as our universe expanded in size the length of that minimum vibration (perhaps infinite at point zero) would have expanded, and therefore created the illusion of time and the speed of light, which, as the universe expands, will continue slowing down. perhaps we are like a big balloon and we have been blown up and all the fields/particles-without-size are vibrating more and more in that space.. am i missing something obvious here? I have seen the word 'only' placed both before and after a noun. Where should the word 'only' go in this sentence? Is it the writer's choice?   If you have attended every lesson, only the songs need to be rehearsed at home. If you have attended every lesson, the songs only need to be rehearsed at home. How to detect if any specific drive is a hard drive? In C# how do you detect is a specific drive is a Hard Drive, Network Drive, CDRom, or floppy? Broken URL for data.stackexchange.com help page What is the fastest lens available for a DSLR? I've seen references to f1.2 lenses. I was wondering, are there any faster lenses available for a DSLR mount? Non-linearity and self-coupling of gravity I have heard that non-linearity of  has to do with the fact that gravity self-couples. What does non-linearity have to do with self-coupling? I have two tables, both with start time and end time fields. I need to find, for each row in the first table, all of the rows in the second table where the time intervals intersect.  For example:             &lt;-----row 1 interval-------&gt; &lt;---find this--&gt; &lt;--and this--&gt; &lt;--and this--&gt;   Please phrase your answer in the form of a SQL WHERE-clause, AND consider the case where the end time in the second table may be NULL.  Target platform is SQL Server 2005, but solutions from other platforms may be of interest also. How to run a command that involves redirecting or piping with sudo? If A and B are symmetric is AB=BA true? Question  if we have matrices $A$ and $B$ which are symmetric. Both of these satisfy: $$  A=A^T$$ Is $AB=BA$ true ?  Attempt to solve  Now if $A$ and $B$ are symmetric then $AB$ most be symmetric too.  $$ AB=(AB)^T=B^TA^T=BA $$  problem is how do you proof that if $A$ and $B$ are symmetric also $AB$ is symmetric ?  If somone could provide some insight on this that would ge highly appreciated.  Thanks,  Tuki When you have a link from lets say twitter that is t.co/foo that links back to your website how does that effect SEO and how do the major search engines handle Shortened URLs? Is it always true that $(A_1 \cup A_2) \times (B_1 \cup B_2)=(A_1\times B_1) \cup (A_2 \times B_2)$ How to "cat" or "less" a libreoffice writer .odt file? I would like to know how to upgrade from my current version of Ubuntu to the next stable from the Command line interface? Word for person who looks for flattery What word could be used to describe a person who seeks and seems to depend on constant positive feedback from the people around him.