Recent content by tsang

I got one example on my notes about PID and maximal ideal. I feel it is a strange example as it doesn't make sense to me, and there are no explanations. It says: For a prime p\in\mathbb{N}, denote by \mathbb{Z}_{(p)} the subring of \mathbb{Q} given by \mathbb{Z}_{(p)}={\frac{m}{n}...

Hi Norwegian, thank you so much for your reply. It is very clear, thank you. I have another question now, that for example 13=(3+2i)(3-2i), but since my goal is decompose 13 into irreducibles, how do I show (3+2i) and (3-2i) are irreducibles, so they cannot be decomposed further? Do I have to...

Hi everyone, I always have trouble on decomposing number into irreducible factors inside Gaussian integer field. I keep trying to express number as product as (a+bi)(c+di), and trying to solve a,b,c,d inside of integers (Z), then see if they are irreducibles, which of course end of very messy...

Homework Statement Let R be a unital ring. Define J(R)={a \in R| 1-ra is a unit for any r \in R} Show that J(R) is an ideal in R. (It is called the Jacobson ideal of R) Homework Equations I is ideal of ring R , then I satifies a+b \in I \forall a,b \in I ra \in I...

Hi everyone, I need a lot help on how to find automorphisms on these particular Cayley graphs. I have three groups here: <a,b,c,d | [ab,cd]=1>; <a,b,c,d | abcda^(-1)b^(-1)c^(-1)d^(-1)=1>; <a,b,c,d | [a,b][c,d]=1>. I finally got three Cayley graphs down, first one is like Z^2, but with...

Hi friend, may I ask you to explain details please? I never seen this formula before, and I have no idea how to use it. Could you please give me a simple example? For example, I saw a question talks about the dipole moment for three metal balls which are connected on three coners of a...

Hi,can anyone tell me how to calculute magnitude and direction of the electric dipole moment of a system? If the system is a bit complicated? What kind of formula I suppose to use? \vec{p}=q\vec{d}?

Can anybody help me that how to work out the direction of Lorentz Force? Should I work out from the formula? Thanks.

Homework Statement Let f: R\rightarrow R be a differentiable even function. Prove that f' is an odd function. Also, prove that if f is a differentiable odd function, then f' is an even function. Homework Equations The Attempt at a Solution I tried to use definition, so I should...

Do I have to do something like connecting circuit for short period to charge capacitor, then let it discharge or something like that? Can I connect capacitor straight to battary without resistor in the series circuit?

Can anyone please give me some suggestions? Thanks a lot.

Thank you,dear friend. But could you please give me more help on details? I truly have no idea about it. I actually don't know which formula to use for Part (a). About Part (c), do you mean by I should think about torque? since one side would be positive and the other side would be negative...

Hi everyone, I'm trying to solve this prac design, but still don't know what to do, can anyone please give me some suggestions? You are given an old cardboard box from Faraday’s, the bargain supermarket for electrical enthusiasts (“Everyday Low Charges”). The box contains  a battery, ...

Homework Statement Three metal balls with unequal radii R1 < R2 < R3 are placed at the vertices of an equilateral triangle, whose sides have length a. The balls are connected by thin metal wires. A positively charged rod is brought into contact with one of the balls and transfers an amount of...