Ring Definition and 1000 Threads

Alright, suppose you managed to build some type of massive ring around the Earth; concentric to the Earth, that is. I'm picturing a continuous metal pole-type object, bigger than Earth and its atmosphere, suspended around the Earth like a ring of a gyroscope. What would the effect of Earth's...

Hello everybody, I'm a bit stuck here. I have a problem tha goes like this: Let R be a principal ideal domain (PID). Let D a subset of R which is multiplicatively closed. Show that the ring of quotients D^(-1)R is a PID too. I've tried several different ways but I couldn't get to the...

Homework Statement \psi_{n}(\theta)=A_{n} \exp(\imath n \theta) where n is an integer Calculate the factor A_{n} if the wave function is normalized between \theta = 0 and \theta = 2\pi. Homework Equations NA The Attempt at a Solution 1=\int_0^{2\pi} |\psi_{n}(\theta)|^2...

I can't seem to make the necessary connections in this problem. Complete the algebra to show that the period for a thick ring ( the difference between the outer and inner radius is very large) is: T = 2π √[(d/g) + ((ΔR)^2/4Rg)] d= diameter of the ring ΔR=Ro-Ri Ro (outer radius)=...

Homework Statement Suppose that f:R->Q (reals to rationals) is a ring homomorphism. Prove that f(x)=0 for every x in the reals. Homework Equations Homomorphisms map the zero element to the zero element. f(0) = 0 Homomorphisms preserve additive inverses. f(-a)=-f(a) and finally...

Homework Statement We've been set an essay question in our first year modern physics course to explain (very basically) how the LEAR at CERN measures the effects of gravity on anti-protons. (I've only just started my first year course so please try and keep things as simple as possible!)...

Homework Statement Find all ring homomorphisms \phi: Z \rightarrow Z \phi: Z2 \rightarrow Z6 \phi: Z6 \rightarrow Z2 Homework Equations A function \phi: R \rightarrow S is called a ring homomorphism if for all a,b\inR, \phi(a+b) = \phi(a) + \phi(b) \phi(ab) = \phi(a)\phi(b) \phi(1R)...

Homework Statement Prove that \phi : Zp \rightarrow Zp, \phi (a) = a p is a ring homomorphism, find the ker \phi Homework Equations The Attempt at a Solution So show that a _{p} + b _{p} = (a + b)p? and (ab)p = (ap)(bp)?

Homework Statement Let R be a ring that satisfies a^2 = a for all a in R. Prove that R is a commutative ring Homework Equations The Attempt at a Solution My attempt at this solution is (ab-ba)^2 = (ba-ab)^2 is true for any ring R => (ab-ba) = (ba - ab) => 2ab = 2ba => ab = ba. The...

Homework Statement Let R be a ring. If any x in R satisfies xx=x, prove that R is a commutative ring. [1 is not necessarily in R in the definition of ring according to this particular book] Homework Equations The Attempt at a Solution I made some attempts but failed. I have...

did anyone else happen to notice it as well? I believe is was on the night of the 13th. It got more and more Intense as the night went on. Beautiful none the less! Anyone know why it happened? I used to remember the reason I thing but now I can't recall it. Oh. And I was in the central nj area.

Ok, I'm given this polynomial and I'm asked to find the roots of it in the ring mod p. And then it asks to do it in, mod p^2, mod p^3 and mod p^4. I don't remember ever learning how to do it in those powers. Any tips on how to solve such things? Note: Without having to sub in all the...

Homework Statement confirm that wavefunctions for a particle in a ring with different values of of the quantum number m are mutually orthagonal. Homework Equations wavefuntion = e^imx [b]3. The Attempt at a Solution i know for the 2 wave functions to be orthogonal their integral...

The definition of R-algebra and R-module looks somewhat similar when R is a commutative ring. For instance, R[x] is both an R-algebra and R-module. I'll appreciate if anyone shows an example which is an R-algebra but not an R-module, and vice versa. Thanks.

Can anyone explain how this works? Couldn't believe it was air in the water when I first saw it. But it appears to be genuine. I know some deal about quantum theories but am stunned like a dog in front of a mirror by these bubbles in the water - help me out!

Homework Statement Let R be a ring and x in R such that x^n=0 for some n show that 1 + x is a unit. I know then that x is a zero divisor and I need to find y such that y(1+x) = 1. I can see in examples that this works and I can prove it for Z mod n. I can't figure out how to prove it...

Solution to diff. eqn as a ring(killing me - please look at my result!) Homework Statement I am presented with the following problem given the direction field f(u,v) = \left( \begin{array}{ccc} -sin(u) & sin(v) \\ cos(u) & cos(v) \end{array} \right) as \left( \begin{array}{c}u^{'} &...

Homework Statement Let N = AB, where A and B are positive integers that are relatively prime. Prove that ZN is isomorphic to ZA x ZB. The attempt at a solution I'm considering the map f(n) = (n mod A, n mod B). I've been able to prove that it is homomorphic and injective. Is it safe to...

For a ring of charge centered about the origin, how would you calculate the charge experienced by a point within the ring of charge but not at the center? So, I know for a ring of charge dE_x = kdq / r^2 = (k*lambda*ds) / r^2 where ds is the arc length. Then what do I integrate over? And does...

Homework Statement This is a fairly easy problem, conceptually... but I can't seem to put the numbers together correctly. A circle with a radius "r" has a linear charge along the circumference with a charge density of \lambda=\lambda_{0}\sin(\theta), where \lambda_{0} is the max charge...

Homework Statement You somehow manage to get a gold ring with inner diameter 2.26 cm stuck on your finger, even though your knuckle has a diameter of 2.3 cm. The temperature of the ring is 23 degrees C. To what temperature would you have to heat the ring in order to get it off your finger...

Hopefully quick/easy question. I am modeling essentially a flat plate under pressure load in ANSYS with a large thermal change. With fixed or simple support at the outer edges, of course the thermal stresses are crazy high. To try and get a better estimate of stresses without modeling the...

Homework Statement A ring of radius 18 cm that lies in the yz plane carries positive charge 6x10^-6 C uniformly distributed over its length. A particle of mass m that carries a charge of -6 \muC oscillates about the center of the ring with an angular frequency of 29 rad/s. Find the...

Homework Statement Given a set R={x,y,a,b} There are 2 tables shown: one is the addition of x,y,a,b elements with x,y,a,b elements. The 2nd table is multiplication of each element with the other elements. (The 2nd table shows that x multiplied by anything equals x) we have a+b=y and (a)(b)=y...

my question relates to the axisymmetrical ring vortex. i know that vorticity must remain constant within a tube, (helmholtz vortex theorem 2) so does that mean that the vortex lines on the outside of the ring are longer (spinning faster) than the ones on the inside? also is that what makes...

Homework Statement Determine the B field at a point P with distance d from centre of current ring radius r (d>r ie outside ring of current) but IN the Plane of ring (i.e off the axis) Homework Equations Biot savart: db=(u.I/4pi.r^2).dl.sinx u=mu, I=current, x=angle made with...

A rather small number of photos we have this week, but will it make choosing for which one to vote for any easier? Please vote for the picture that best represents our theme, which is a scene at a wedding. 1. hypatia 2. binzing 3. Andre...

With This Ring, I Thee Wed This time, it is on weddings! Your picture must depict scenes at a wedding. This includes the scenes at the actual ceremony and the reception. Note that pictures on items related to a wedding without showing that they were taken at the wedding site is not...

Let A be a ring. If every finitely generated right ideal is genreated by an idempotent then Jac(A) =0. Here Jac(A) means jacobson radical. Proof: Let a be in Jac(A) and pick an idempotent element e such that Ae = Aa, thus a = ae and e=xa for x in A. Hence a =axa so a(1-xa)=0. Since...

Let A be semiprime ring and e a non-zero idempotent. If Ae is a minimal left ideal then eAe is a division ring. Proof: Suppose that Ae is a minimal left ideal and that exe is different from 0 for x in A. Then $Aexe \subset Ae$ since Ae is an ideal and since Ae is minimal hence...

Homework Statement A wire is reeled on a ring (radii R_{1} and R_{2}). Find the induction of a magnetic field in the middle of the ring, if there is a current I through the wire and there are N waps. Waps are reeled very tightly in only 1 layer. Homework Equations H=\frac{IN}{l} B=\mu HThe...

Homework Statement Consider a thin ring of mass m that has a radius a and negligible width. The ring lies in a horizontal plan. The ring is an insulator and carries a fixed charge q that is uniformly distributed around its circumference. The ring is located in a magnetic field of strength B_0...

Hey, It's been about a year since I took mechanics, and I had agreed to help a friend out today. She gave me this problem, and I'm drawing a blank at how to approach it. No solution necessary, just an approach! Homework Statement A thin, uniform ring of mass m and radius R is attached by a...

Homework Statement Prove that Q[x]/\langle x^2 - 2 \rangle is ring-isomorphic to Q[\sqrt{2}] = \{a + b\sqrt{2} \mid a,b \in Q\}. The attempt at a solution Denote \langle x^2 - 2 \rangle by I. a_0 + a_1x + \cdots + a_nx^n + I belongs to Q[x]/I. It has n + 1 coefficients which somehow map...

Homework Statement Okay, I totally do not understand how to derive the electric field made by a dipole or a line or a ring or etc. Homework Equations When finding the electric field, when you make an estimate, saying that the test charge is very far away, it should be similar to kQ/r^2...

Homework Statement A ring (hollow cylinder) of mass 2.30 kg, inner radius 4.35 cm, and outer radius 5.65 cm rolls (without slipping) up an inclined plane that makes an angle of θ=38.0°, as shown in the figure attached. At the moment the ring is at position x = 1.95 m up the plane, its...

Homework Statement The linear charge density for a ring of radius R which lies in the xy-plane (center at the origin) is given by: \eta(\phi) = \left\{ \begin{array}{c l} +\lambda & \mbox{if } 0<\phi<\frac{\pi}{2} \\ - \lambda & \mbox{if } \frac{\pi}{2}<\phi<\pi \\ +\lambda &...

Moment of Inertia Hello community members, Can anyone let me know, the moment of Inertia formula (I) for a ring with inner radius (R) and height (h). Thickness can be considered (t). Awating response... Kind regar

[SOLVED] Moment of inertia of a sign consisting of ring and rectangle Homework Statement A sign is formed from two uniform discs,each of mass 0.25kg and radius 0.2m,rigidly,fixed to a uniform rectangular lamina ABCD at A and D. This dis attached at A has diameter AE and BAE is a straight...

hi , pleasehelp me itry to soution this question but ican not , because this out my book Show that a proper ideal I of a commmutative ring R is a maximal ideal iff for any ideal A of R either A subset of I or A+I=R

Homework Statement A metal ring 4.50 cm 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 produce an initial uniform field of 1.12 T between them but are gradually pulled apart, causing this...

Hi, I was hoping someone can verify this for me. In uni today we had to calculate the magnetic field of a ring of current, lying in the xy-plane. First we had to calculate it on the z-axis (perpendicular to the ring) which was easy. Then we had to calculate it on the y-axis (in the plane...

A thin charged (charge=Q) ring of radius a centered on the z axis lies in the x-y plane. The potential outside the ring is given. Now the ring is placed inside a grounded conducting spherical shell of radius b > a. What is the potential inside the ring and between the ring and the sphere...

Can anyone explain how flying ring works? like the demostration whith a magnetic coil connected to AC poer and an aluminum ring. the ring was placed on the top of the coil and althought aluminum is a non magnetic, the ring was thrown to the ceiling. can anyone tell me why there was force on...

Let M be a compact manifold and C(M), C^{\infty}(M) denote rings of continuous (resp. smooth) real functions on M. Let m be a maximal ideal of functions vanishing at some point x_{0} \in M. Prove that m is finitely generated over C^{\infty}(M), but is not finitely generated over C(M).

Dear all, I would like to ask a question regarding advanced materials. I am currently working with benzoyl film and its conductivity. When a conductivity test was performed against the benzoyl film after it was heated up gradually, it showed increase in the conductivity accordingly until...

[SOLVED] Electromagnetic induction Homework Statement You are given the following apparatus: copper ring, battery, variable resistor, lengths of insulated copper wire with connecting terminals at each end. Describe, how you would use all of this apparatus to induce a current in the copper...

"Derivative" in an abstract polynomial ring Homework Statement Let R be any ring and define D:R[X]-->R[X] by setting D[\sum a_nX^n]=\sum na_nX^{n-1}. a) Check that, if f(X)=\sum a_nX^n and g(X)=\sum b_nX^n, then D[f+g]=D[f]+D[g] b) Check that...

How do you proove what the idempotents of the ring Z/100Z are? I know by trial and error that they are the elements 0,1,25,76 but have no proof as to why this is. i know i have to find the integers 'a' such that 100 divides a(a-1)=a^2 -a but can do the maths to get a proper reasoning any...

Homework Statement If a,b,c,d \in R, evaluate (a+b)(c+d). (R is a ring. Homework Equations The Attempt at a Solution I think that it's simple foiling, but I'm not sure. ac+ad+bc+bd