Ring Definition and 1000 Threads

Some Japanese tech company called shimizu is parading this new idea of solar energy generation. The Luna Ring it is called. Links http://news.cnet.com/2300-11386_3-10003698.html" http://www.youtube.com/watch?v=TUL_rDeKIeU" I think there are some serious issues with said idea WRT...

Homework Statement Determine whether the indicated operations of addition and multiplication are defined (closed) on the set, and give a ring structure. If a ring is formed, state whether the ring is commutative, whether it has unity, and whether it is a field: The set of all pure...

Homework Statement Describe all the units (if any) in each given ring: 2Z X Z with addition and multiplication by components; and Z X Q X Z with addition and multiplication by components Homework Equations The Attempt at a Solution I do not know how to begin, I am not sure how...

Homework Statement Give an example of a commutative ring R with a 1 and nonzero prime ideal P of R such that P = P2 Homework Equations The Attempt at a Solution Letting R be an integral domain and look at the ideal 0xR in RxR. is all i got but not sure how to show this or what to...

Hi, given a polynomial ring R=\mathbb{C}[x_1,\ldots,x_n] and an ideal I=\langle f_1, f_2 \rangle, \quad f_1, f_2 \in R, is it always true that R/I \cong (R/\langle f_1 \rangle)/\phi(\langle f_2 \rangle), with \phi: R \rightarrow R/I being the quotient map? That is, is quotienting by I always...

Homework Statement A metal ring 4.50cm in diameter is placed between the north and south poles of large magnets with the plane of its area perpendicular to the magnetic field. These magnets initially produce a magnetic field of 1.12T, but are gradually pulled apart, causing the field to remain...

Hi everyone. I want to derive for fun the stationary state wave functions for FREE a particle of mass m on a ring of radius R. The question seems trivial, but I am getting hung up on something silly. What I think I know: Since \psi can be written as a function of the radial angle \phi ...

1)Problem statement A translating and rotating ring of mass 1 kg, angular speed of 500 rpm, and translational speed of 1 m/s is placed on a horizontal surface. The coefficient of friction between the ring and the surface is 0.35. Outside radius is 3 cm. This is a problem from a FE...

Homework Statement A thick cylindrical ring of inner radius 29.0cm and thickness 2.8cm has a mass of 10.0kg. What is the moment of inertia of this cylinder about its central axis? Homework Equations I = (.5)(m)(ri^2+ro^2) The Attempt at a Solution I tried to use hollow cylinder...

Homework Statement There wasn't a figure given. All that was given was that the figure is a circular ring. Theta is the angle between the electric field direction and a unit vector normal to the surface area of the ring. Flux versus costheta was plotted and a slope was found to be m = 0.172. E...

Homework Statement The ring (m), which weighs 5Kg, is sliding along a frictionless arc (Shown in the draw). Arc radius - 1.2 meters. There are 2 forces applied on the ring: 1) F - 40N and always tangent to the circle. 2) F' - 150N, 30 degrees above the horizon. Calculate the total...

Homework Statement A long circular solenoid of radius a and N turns per unit length has its axis in the z direction. A small highly conducting ring, or area A, resistance zero but self inductance L, is place with its plane horizontal and its centre on the axis and near the top of the...

1. Prove that a ring which is left Artinian and right Noetherian is right Artinian. The Attempt at a Solution I can't figure it out. Can anyone help?

Homework Statement If s is a ring with the property that s=s^{2} for each s\in S, which of the following must be true? I. s + s = 0 for each s in S. II. (s+t)^{2}=s^{2}+t^{2} for each s,t in S. III. S is commutative Homework Equations none The Attempt at a Solution The answer is I, II...

Hello Experts, Again a Q and what I did, please tell me what I am doing wrong: Given that there is a ring of matrices above Z (integers) Mn(Z) and 2 ideals I, J of this ring. I need to prove that they are commutative: IJ = JI What I did is that: For all i in I and for all M in...

Hello Experts, Here is the question, and what I did: Q: Given a ring with division D char(D) != 2, F = Centralizer of D (means that F becomes a field). Given that x in D isn't in F but x^2 is included in F. Needed to prove that there exists y in D and y*x*y^(-1) = -x and also that y^2...

Homework Statement A total charge q is distributed uniformly along a ring of radius b. The ring is in the x-y plane centered on the origin. The multipole expansion is not valid for r<b. Find an expansion for the potential valid in this regionHomework Equations The charge density is just...

Homework Statement A uniform circular ring of charge Q= 6.40 microCoulombs and radius R= 1.30 cm is located in the x-y plane, centered on the origin as shown in the figure. Homework Equations 1.What is the maximum value of E on the z-axis? 2.What is the frequency of the small...

Homework Statement Determine the nilpotent, idempotents and units in a) F[x]/<x2-x> b) F[x]/<x2> Homework Equations The Attempt at a Solution How do I do this without a specified Field? For a) the elements in R would be {a+bx: a,b are in F; x2=x} b) {a+bx: a,b in F; x2...

Show \mathbb{Z} [ \sqrt{2} ] = \{ a + b \sqrt{2} | a,b \in \mathbb{Z} \} has infinitely many units. I started by taking an element: a + b \sqrt{2} \in \mathbb{Z} [ \sqrt{2} ] and finding an inverse \left( a + b \sqrt{2} \right) ^{-1} such that the product gives zero and...

Homework Statement Given a commutative ring R with a prime characteristic p, show that the mapping phi:R-->R defined by phi(a)= a^p is a isomorphismHomework Equations Fermat's little theorem(I think)The Attempt at a Solution I'm pretty sure Fermat's theorem must have something to do with this...

Homework Statement a) Calculate the electrostatic force on an uniformly charged rod of length 2L and charge q, which lies along the axis of an uniformly charged ring of radius R and charge q'. The centers of the charged rod and the rings are displaced at a distance z= z0. b)Show that if z0 >>...

I was asked to decide if Z_9 and the direct sum of Z_3 and Z_3 are isomorphic. Do I check to see if they are 1-1 and onto?

Homework Statement Let R = Z[x] be a polynomial ring where Z is the integers. Let I = (x) be a principal ideal of R generated by x. Prove I is a prime ideal of R but not a maximal ideal of R.Homework Equations The Attempt at a Solution I want to show that R/I is an integral domain which...

My professor gave us this query at the end of class, it contained two parts. 1. Show a ring is idempotent 2. Consider the degree one polynomial f(x) is an element of M2(R)[x] given by f(x) = [0 1 ______0 0]x + B (so f(x) = the matrix []x + B). For which B is an element of M2(R), if any...

Homework Statement A wire with uniform charge density λ per unit length is bent into a ring of radius a and rotates with angular velocity ω about an axis through its centre and perpendicular to the plane of the ring. Find the magnetic field on the axis at a distance z from the ring...

Homework Statement Let (X,T) be a normal topological space. Let R be the ring of continuous real-valued functions (with respect to the given topology T) from X onto the real line. Prove that the that T is the coarsest Topology such that every function in R is continuous. Homework...

Homework Statement I am try to prove : Let R be a ring, I be a ideal of R. Then N is a maximal in R/I if and only if N=M/I where M is a maximal ideal in R that contains I. Homework Equations The Attempt at a Solution First I'm not 100% sure that the statement is true, but I'm...

I'm working with elementary rings, and my professor gave me about ten of these to start but it seems like a lot of work with how he managed it. I know you guys don't answer homework so I chose so I can do the others. Any help would be greatly appreciated, the groups were easy but the rings are a...

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...

"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 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...