Ring Definition and 1000 Threads

Homework Statement Let R be a commutative ring and let fa: R[x] -> R be evaluation at a \in R. If S: R[x] -> R is any ring homomorphism such that S(r) = r for all r\in R, show that S = fa for some a \in R. Homework Equations The Attempt at a Solution I don't get this at all...

Homework Statement I'm doing a report on an electron diffraction experiment, where a carbon crystal is used as a diffraction grating. There are two line spacings d1, and d2. Observed in the experiment in two cocentric rings. What I'm unsure about is which spacing correlates to which spacing...

"smoke" ring with only air? Can "smoke" ring be blown with only air (withouth smoke) in cold?

Hi, I found a couple of proofs proving that 1=0 only in the trivial ring {0}. They say Suppose 1 = 0. Let a be any element in R; then a = a ⋅ 1 = a ⋅ 0 = 0. But what I don't understand is that they say a = a ⋅ 1. But that is only true if a ring has unity (x*1=1*x=x), and it is possible to...

Is it possible to levitate a magnet in a superconducting pipe or a ring? Is it possible to try to calculate this using the method of images and treat the magnet as a little current loop? Any input will be much appreciated.

I got a question that has a charged ring, with two lines of charge that intersect it. So it looks like a circle with a cross in it. I am asked to give the electric field. Would it just be the sum of each of the electric field from each part? So Etotal= Ering + Eline + Eline

When solving Schrodinger's eqn for a quantum ring, what would be the boundary conditions? The solution (polar) should be Ψ(Φ) = A exp(ikΦ) + B exp(-ikΦ) And I believe the boundary conditions are Ψ(0) = Ψ(2pi) Ψ(0) = A + B Ψ(2pi) = A exp(ik*2π) + B exp(ik*2π) and I suppose I can...

Homework Statement A ring of charge with radius R = 0.5 m is centered on the origin in the x-y plane. A positive point charge is located at the following coordinates: x = 19.0 m y = -14.6 m z = -2.6 m The point charge and the total charge on the ring are the same, Q = +40 C...

Let A = k[x,y,z] and Y = \{(t,t^2,t^3)|t \in k\}, which is irreducible. It corresponds to the prime ideal p=(y-x^2,z-x^3). A(Y) is generated by x,y,z of degree 1 as a k-algebra in its graded ring structure. Each group corresponding to the degree d is spanned by the linearly independent...

Hello! This is probably a really asinine question. I was trying to identify an area of a ring, namely a really small ring such that its near enough the circumference of a circle. I thought I could approach it in two ways. The first was to subtract a smaller circle of radius r1 form a circle...

Brian Cox on Wonders of the Solar System (episode: Order Out of Chaos) on the Science Channel says the rings of Saturn are made up of chunks of water ice. Water ice? In space? I would expect a chunk of water ice in space would experience a near zero vapor pressure. Wouldn't it? And if...

i am a last year EE student and I am creating a library in simulink. and at 1 stage i need to simulate a ring oscillator . i ve done it but with a lil bit of problems in the simulations. I am using spice parameters for simulink . that's why i asked if any of you guys have done it before. how do...

Negative permeability of split ring resonators(SRR) is obtained between the resonant frequency and the Plasma frequency of the SRRs, then what is the meaning 'eigenfrequency' of split ring resonator(SRR). Is eigenfrequncy is that 'frequency' at what negative permeability occur ??

Hello (this is not a homework) I have a doubt about the ring oscillator. I have to create a R.O. with a frequency of 10kHz, now I know i have to link an odd number of inverters in a ring form, but using the formula of (f=1/2*n*Tp) it gives me a frequency in the Megas, I've red you can use a...

Homework Statement Consider a circular ring of radius r, uniformly hcarged with linear density lambda. Find the electric potential at a point on the axis at a distance x from the centre of the ring. Using this expression for the potential, find the electric field at this point. Homework...

Homework Statement I need to show that two elements in \textbf{Z}[\sqrt{-5}] have gcd = 1. The elements are 3 and 2+\sqrt{-5} Homework Equations The Attempt at a Solution My way of thinking was if I can show that both elements are irreducible, then they are both prime and hence...

Homework Statement A bead rests on smooth vertical ring of radius R. Bead is given a slight push so that it slides down around the ring. At some instance the bead is at angular position θ with vertical then choose correct option from the following A. acceleration of bead is vertical at θ =...

Homework Statement An originally complete ring made of linear elastic material (Young's modulus, E and Poisson's ratio, v) is cut by a saw. A gap, delta, is generated by a pair of forces, P. Determine this force, P. (Use Saint Venant's principle) Inner radius of ring, a. Outer radius, b...

Homework Statement A thin, non-conducting ring of mass m, carrying a charge q, can rotate freely about the axis. At the instant t=0 the ring was at rest and no magnetic field was present. Then suddely a magnetic field B was set perpendicular to the plane. Find the angular velocity acquired by...

Homework Statement A thin semicircular conducting ring of radius R is falling with its plane vertical in a horizontal magnetic field B (see fig). At the position MNQ, speed of the ring is v and the potential difference developed across the ring is - (options are given)The Attempt at a Solution...

I was going back to a previous chapter to study for my finals, and came across the field of charge around a ring problem. Basically, it's designed to show how using a special case can make a problem easier. This was one of those equations I just kind of had to memorize and use. I'm the kind of...

Homework Statement a) What is the E-field at the center of a metal ring which has uniform charge density? b) Is E=0 for any other point within the circumference of the ring?2. The attempt at a solution For (a), since the ring has uniform charge density and is symmetrical, based on symmetry...

I have to find the E field at all points on the z-axis for a ring of charge with radius = R. \lambda(\phi) = \lambda_0 cos(\phi) where 0 \leq \phi < 2 \pi I know how to do the problem when it is the charge per length is uniform but when I do the calculation for the non-uniform case I...

I am doing a discrete event simulation of logic gates and I have come upon a problem. I have set up a system similar to a ring oscillator. I understand that this system should not oscillate, but after thinking about it, I'm not sure why not. The system has one input, 1 fed into a NAND gate. The...

Hi I have some conceptual questions about one situation. I have posted the picture. We have a bead on a ring which is rotating about the vertical axis passing through its center. The bead is not tied to the center of the ring , though it appears like that in the figure. Let m be the mass of...

Let R be a discrete valuation ring with fraction field F. I believe it's straightforward to show that any torsion-free module M with the property that M \otimes_R F is a finite dimensional F-vector space is of the form R^m \oplus F^n. What if M \otimes_R F is infinite dimensional?

Hi I was thinking about this conceptual problem. Consider a thin ring of radius R, which is rotating about the axis passing through its center of mass. Now let's says there is no gravity and the ring is rotating at some constant angular velocity \omega , so the angular momentum is conserved...

Homework Statement Compute the speed of debris seen hitting the inner ring of Supernova 1987A. Assume radius of inner ring is 0.7 light years. Homework Equations The Attempt at a Solution I'm not quite sure where to start. I thought about just using kinetic energy = 0.5mv^2 because I...

Homework Statement if R is a finite ring, then the characteristic of R is a divisor of | R |. Homework Equations The Attempt at a Solution Can this be proven using lagrange's and char R is the subgroup and R is finite group, then the order of char R is a divisor order of R, and i...

http://yfrog.com/ea1c281p http://img514.imageshack.us/img514/3479/1c281.png Uploaded with ImageShack.us Homework Statement A circular ring of fine wire carries a uniformly distributed positive charge q. Find the magnitutde and diretion of the electric field at the center of the...

Onto ring homomorphism C-->R Why can't there be an onto ring homomorphism from the Complexes to the Reals? The only property of the complexes that the rations don't have that I can think of is the guarantee of square roots- but I can't see how that would interfere with an onto function.

Homework Statement Let {p_n}n>0 be the ordered sequence of primes. Show that there exists a unique element f in the ring R such that f(p_n) = p_n+1 for every n>0 and determine the family I_f of left inverses of f. Homework Equations The ring R is defined to be: The ring of all maps...

Homework Statement Two questions really, the first is about the ring of quaternions H and the second about a set of maps. a) Find an element c in H such that the evaluation phi_c : C[x]-->H is not a ring homomorphism. In words that is: "the evaluation phi sub c from the ring of complex...

Homework Statement Let R = { [ a + b*sqrt(m) c + d*sqrt(m) ] } [ n(c - d*sqrt(m)) a - b*sqrt(m) ] (Sorry if the matrix is unclear... I can't get it space nicely. r11 = a + b*sqrt(m) r12 = c + d*sqrt(m) r21 = n(c -d*sqrt(m))...

Is there something you can do to a ring to produce a commutative ring? Like for any group, you can create an Abelian group by factoring out its commutator subgroup. Can you "force" a ring to commute?

I have just learned about an interesting cultural difference. On which hand/finger do you wear your wedding ring?

Electric potential at point x on the axis of a ring of charge density "eta" Homework Statement A circular disk of radius R and total charge Q has the charge distributed with surface charge density \eta = cr, where c is a constant. Find an expression for the electric potential at distance z on...

Homework Statement Calculate (5^7)-(7^7)+(9^7)-(11^7) in Mod24 Homework Equations The Attempt at a Solution I added all the bases and got -4 (which I changed to 4), then I took 4^7 and ended up with 16,384. I divided 16,384 by 24 as many times as I could, which gave me an end...

I know this isn't just a simple problem, and it depends on a lot of things like the critical magnetic field at various temperatures, etc. And I'm still learning to calculate things like inductance and how that (eventually) relates to power. But suppose there were a material that was a...

How would we show that R X R X R X R is not isomorphic to M(R) with R being the set of real numbers. And more generally, what does it mean for one ring not to be isomorphic to another

Hi, I am trying to work out the resonant frequency of an annular ring, does anyone know a general equation for it? For example the ring has an outside diameter = OD and inside diameter = ID. The ring is gently clamped at the outside diameter and a force F applied evenly at the inside...

Homework Statement Calculate 7*11 + 9*11^-1 in the group Z20 Homework Equations The Attempt at a Solution 77+ (9*1/11) in group Z20 77 + 9/11 17 +11x= 20mod+9 My solution was 12, this makes 149 on both sides when you multiply the mod times 7. I am doing independent study...

Homework Statement Make four calculations in the group Z7 -------------------------------------------------------------------------------- First, calculate in Z7 6 - 3*5 = Homework Equations The Attempt at a Solution 6-15=6-1=5 =2 The program I am using...

Abstract algebra--> Let R be a ring and let M2(R) be the set of 2 x 2 matrices with Homework Statement Let R be a ring and let M2(R) be the set of 2 x 2 matrices with entries in R. Define a function f by: f(r) = (r 0) <----matrix ...(0 r) for any r ∈ R (a) Show that f is a...

Homework Statement Let R be a field and f : R->R be a ring homomorphism prove that f(r)=0, for all r in R, or f is injective Homework Equations n/a The Attempt at a Solution or alternative ways i have to prove (Kernel of f)=R or (kernel of f)={0} i've tried but stuck somewhere, hmm and...

Homework Statement We are given a ring of charge in the xy plane with a line density of λ(φ)=λ0cos(φ). Here φ is measured as a rotation from the +x axis. First, calculate the electric potential along the z axis. Then, calculate the electric field along the z axis. Hint: The problem may...

Homework Statement Let R be a commutative ring, c \in R, M is ideal in R prove that J=\left\{rm+c\ |\ m \in M \ and\ r \in R \right\} is ideal in R Homework Equations n/a The Attempt at a Solution for non-emptiness is easy so i want to show any x=rm+c, y=r'm'+c...

We have E the set of even integers with ordinary addition Define new multiplication * on E defined as a*b = ab/2 where on the right hand side of the equation is just normal multiplication. I am just a bit confused i am trying to show Associative multiplication meaning i have to show (a*b)*c =...

If a Eugenol ring was saturated into Cyclohexane, how would this change the flavor? and why? Eugenol is C10H12O2

i cannot understand why persistent current in a normal metal ring threaded by a magnetic field is a surprise. the hamiltonian is H=\frac{1}{2I}\left(-i \frac{\partial}{\partial \theta}-A\right)^2 and the eigenstates are \phi_m(\theta)=\frac{1}{\sqrt{2\pi}} e^{i m \theta} with...