Recent content by NoodleDurh

I only ask, because I noticed that the Euler Characteristic is an invariant and pops up in differential geometry as the G-B theorem. so could some one explain why they are special.

This is what I thought, and ended up forgetting about the zero divisors. So as you said ##\oplus \lim{i \ in I} \mathbb{Z}_{p_{i}}## isn't a field. But still a Ring. I think this is what I am suppose to prove, that theorem you are talking about, because it essentially leads me there. I came...

Yeah, I know this. But if think about them as Rings then, there should exist a isomophism between them. Also, I am not sure I know what a nonzero element would look like. For example, when we are in the Ring ##\mathbb{Z}_{2} \oplus \mathbb{Z}_{2}## we get elements like ##(0,1)## and ##(1,0)##...

okay, yeah you assumption is correct. Also, not to get to far off topic, but what does the p-adic integers look like.

Okay, I thought that there would exist a projection from ##\mathbb{Z}^{p-1}## to ##\mathbb{Z}_{p}## where ##p## is a prime. Like there exist a projection from ##\mathbb{Z}## to ##\mathbb{Z}_p##

Thank for you help... It seems I need to head back to the drawing board. Originally, The problem was: Suppose ##f(x) \in \mathbb{Z}_{p}[x]## and ##f(x)## is irreducible over ##\mathbb{Z}_{p}##. If ##deg f(x) = n##, then ##\mathbb{Z}_{p}[x]/ (f(x))## is a field with ##p^{deg (f(x))}## elements. I...

So, I do not understand how it is not one, or the other. Unless you mean to say it is either injective or surjective, because if ##G_1## is ##S_2## and ## G_2## is ##\mathbb{Z}_{2}##, there is a natural injection isomophism between the two. Yet, if we do take that map ##\phi## and look at ## S_2...

I think I might have figured it out. But, still I do not know when a proof is done. Also, my notation might be strange... ##\mathbb{Z}_{p}## is ##\mathbb{Z} / p ## Since we know that ##|\mathbb{Z}_{p}| = p##, in addtion to knowing that ##|\mathbb{Z}_{p}[x]/(f)| = p^{deg(f(x))}## and ##f(x) \in...

[Bump] Sorry it has been 3 days.

How Do I take projects created in Dev-Cpp and transfer it into Visual C++. I mean they are both C++ projects correct? I tried to open these projects in Visual C++, but they just don't want to open...erm I mean I can't open them. Help?

Okay, you pretty much answered my question. But a follow up question, So if I am going to learn about these langlands programs. What do I need to learn.

What are these Langlands Programs. I am curious.

Homework Statement Show that if ##|\mathbb{Z}_p/(f)| = p^{deg(f(x))}## where the ##deg(f(x)) = n## and ##f(x) \in \mathbb{Z}_{p}## is irreducible over ##\mathbb{Z}_{p}[x]##, then ##\mathbb{Z}_{p}[x]/(f) \rightarrow_{\phi}^{\cong} \bigoplus_{i \in I} \mathbb{Z}_{p_{i}}## where ##|I| =...

I was actually having a similar problem in the past. The determinate just tells us the orientation of the space we are in... better yet, it tells us the orientation of the vectors. hmm... think of the cross product of two vectors, this guy is anti-commutative, yes? This means, ##a \times b = -(b...

Okay, what do you mean. I am using c++ visual studio 08 and I can't figure out where I go to change the project settings, the subsystem linker options so that it accepts my... I don't know how to create a GUI app in VS 08 >///< P.S. I have been having a lot of problems with linking :/ same with...