Ring Definition and 1000 Threads

Homework Statement Give an example of a ring monomorphism f:M(2;R)-M(3;R) Homework Equations The Attempt at a Solution I can't think of anything that would be a monomorphism.

Homework Statement Prove that if f:R-R' is a ring homomorphism, then a) f(R) is a subring of R' b) ker f= f^{-1}(0) is a subring of R c) if R has 1 and f:R-R is a ring epimorphism, then f(1_{R})=1_{R'} Homework Equations For a ring homomorphism, f(a+b)= f(a) + f(b) f(ab)= f(a)f(b)...

Let R = Mn(F) the ring consists of all n*n matrices over a finite field F and E= E11 + E22 + ... + En-1,n-1, where Eii is the elementary matrix(Eij is matrix whose ij th element is 1 and the others are 0). Then the following hold: 1. If A is a rank n-1 matrix in RE then A is similar to E...

Imagine a ring; the image below shows the top cross section of the ring - The arrows represent forces which is acting towards the inner side of the ring cause of a pressure which applies towards it's inner side. Assuming the ring to be made up of a material having a plastic property...

Homework Statement A ring with a 15cm radius and with a uniform charge of 20 micro coulombs is in the yz-plane with the origin at its center. What is the force on a -3 micro coulombs charge on the x-axis at x=5cm? Homework Equations E=kQx/(R^2 + x^2)^(3/2) F=QE The Attempt at a...

Homework Statement Suppose there is an optically thin emitting ring with inner radius r_{in} and outer radius r_{out} seen edge on. Compute the relative surface brightness of the ring as a function of its projected position in the sky. Homework Equations Radiative transfer: dE = I_{\nu}...

Homework Statement A ring-shaped conductor with radius a = 2.20 cm has a total positive charge Q = +0.145 nC uniformly distributed around it, as shown in the figure below. The center of the ring is at the origin of coordinates O. (a) What is the electric field (magnitude and direction) at...

Homework Statement A uniformly charged ring of radius 8.1 cm has a total charge of 118 micro Coulombs. The value of the Coulomb constant is 8.98755e9 N M^2/C^2. Find the magnitude of the electric field on the axis of the ring at 1.15 cm from the center of the ring. Answer in units of N/C...

Homework Statement A uniformly charged ring of radius 8.1 cm has a total charge of 118 micro Coulombs. The value of the Coulomb constant is 8.98755e9 N M^2/C^2. Find the magnitude of the electric field on the axis of the ring at 1.15 cm from the center of the ring. Answer in units of N/C...

I have this question and its a combination of the binomial theorem and nilpotent elements within a ring. Suppose the following, am=bn=0. Is it necessarily true that (a+b)m+n is nilpotent. For this question I did the following: \sumi=0m+n\binom{m+n}{i}am+n-ibi If i=m, then a=0...

Homework Statement A uniformly charged ring has a radius a, lies in a horizontal plane, and has a negative charge given by -Q. A small particle of mass m has a positive charge given by q. The small particle is located on the axis of the ring. What is the minimum value of q/m such that the...

Homework Statement Assuming the mapping Z --> F defined by n --> n * 1F = 1F + ... + 1F (n times) is a ring homomorphism, show that its kernel is of the form pZ, for some prime number p. Therefore infer that F contains a copy of the finite field Z/pZ. Also prove now that F is a finite...

I need a telephone to answer when called, dial a number on another telephone, and then hang up when the caller hangs up. I have both the pick up issue and the dial issue solved. The mail problem is the hanging up after the caller hangs up. I'd be very happy if I did not have to use a...

Homework Statement In this question we have to make use of the chinese remainder theorem and its applications: 1. Let F be a field and let p1(x), p2(x) two irreducible poynomials such as gcd(p1,p2)=1 over F. Prove that: F[x]/[p1(x)p2(x)] Isomorphic to F1 x F2 where F1=F[x]/(p1(x)) and...

If an initially circular ring is made out of round by cutting out a section of the ring (delta g) and compressing the ring till the gap is approx zero is there an equation to describe the eccentricity of the circle? Cheers Gordon

Hi could someone tell me if it is possible to calculate the shear loss from a metal piston ring against the cylinder in a hydraulic pump when the outlet pressure and speed (in rpm) of shaft are known. Cheers (Updated: maybe along the lines of in cylinder pressure x piston speed x friction...

Hi! I have following question. I will explain it with abstract notation although in fact I am working with some peculiar matrices. I have finitely presented noncommutative monoid with identity element I . Presentation of this let say would be M = <S,T;S^2> which means that if S,T are...

Homework Statement Prove that Z with the following addition and subtraction is a ring. Homework Equations a\oplusb = a + b - 1 and a\odotb = ab - (a + b) + 2 The Attempt at a Solution I proved all the axioms for addition. I'm stuck on the multiplication part...

what are all the ring homomorphism from Z[X] to Z[X]. Thank you

I just had this problem on my Electromagnetics final. I want to know if I got this right and I can't find the problem with google. Homework Statement Consider a conducting quarter-ring. It can be envisioned as one piece of a hollow cylinder that has been cut into fourths down its length...

I'm trying to figure out what is the resulting motion when a ball collides with a spinning ring whose center of mass is initially at rest. See attached diagrams. The collision is assumed to be elastic. The ball has unit mass, and the ring has unit mass and unit radius. Shown in the "before...

Homework Statement A particle of mass m is tied to the middle of a light, inextensible string of length 2L. One end of the string is fixed to the top of a smooth vertical pole. The other end is attached to a ring of mass m, which is free to slide up and down the pole. The particle moves in a...

Homework Statement I need to prove this theorem Let R be a commutative ring with identity and c1,c2,...cn E (element of) R Then the set I={r1c1+r2c2+...+rncn|r1,r2,...,rn E R} is an ideal in R Homework Equations Well I do know I need to prove closure under subtraction, closure...

Homework Statement What is the electric potential a distance x above the center of a ring of charge Q with a radius R? Derive the electric field from this relationship.Homework Equations ΔVab=-∫E·ds The Attempt at a Solution

Homework Statement A conducting ring with radius a and mass m is placed in a magnetic field at a height H above the origin of the reference frame. The plane of the ring is parallel to the ground, that is, the normal is directed along the z-axis. The electrical resistance per unit length of...

Homework Statement For a prime p and a polynomial g(x) that is irreducible in Z_{p}[X], prove that for any f(x) in Z_{p}[X] and integer k > 1, [f(x)]^{k} = [f(x)] in Z_{p}[X]/(g(x)). The Attempt at a Solution I realize this is an extension of Fermat's Little Theorem, however I cannot...

I am trying to find any diagrams like the following ones: http://www.valdostamuseum.org/hamsmith/DFblackIn.gif http://www.illc.uva.nl/~seop/entries/sp ... one-bh.gif http://www.orbiter-forum.com/gallery/da ... ration.jpg (the 1st is the best, even I failed to find it in better...

Homework Statement 1.compute the diffraction pattern through a ring aparture, internal radius a, external radius b, wave length lambda. the incoming wave is a monochromatic, plane wave, vertical to the ring plane. 2.how will the diffraction expression change when a->b? 3.near the aparture...

Comparing Rotational and Linear Motion -- block vs. disk vs. ring Homework Statement A disk and a ring, both of mass M and radius R, are placed atop an incline and allowed to roll down. A block, also of mass M, is placed atop the same frictionless incline and allowed to slide down. How do...

Charge Q uniformly spread through the ring of radius a. Find the work done to bring point charge q from the center of ring to infinity along the axis through the center of ring. From a previous problem I calculated E=kQz/(z^2+a^2)^1.5 I then tried to apply the formula W=eo/2\intE^2 dz...

Just interested how this positive charge occurs. Thank you :smile:

Does anyone have experience of calculating piston ring leakage, my problem is that the piston leakage is in a hydraulic system with a flooded cylinder and operating pressures of up to 400bar. All journals I find are on IC engines and so the theory is very different. There are also...

Homework Statement This is a personal enquiry, not a homework question. I think I understand but would like confirmation. In a modified Thompson's Jumping Ring apparatus, the solenoid is horizontal and the ring free to move on the iron core. If the ring is either side of the central...

A charge of 10 nC is uniformly distributed around a ring of radius 10 cm that has its center at the origin and its axis along the x axis. A point charge of 1 nC is located at x = 1.75 m. Find the work required to move the point charge to the origin. Give your answer in both joules and electron...

Homework Statement what is the electric potential a distance x above the center of a ring of charge Q with a radius R surrounded by another ring of charge -Q with a radius 2R? Homework Equations V= kQ/sqr root(a^2+x^2) The Attempt at a Solution I know the above equation would be...

I was trying this mental exercise and I need help and confirmations... so please launch your comments Imagine (as an assumption) that the surface of the Earth is completely flat with no disturbances. A perfect sphere. Imagine that is possible to build a solid ring made of a completely...

Ring of Charge--how to maximize the Electric Field A thin nonconducting rod with a uniform distribution of positive charge Q is bent into a circle of radius R. The central perpendicular axis through the ring is a z-axis, with the origin at the center of the ring. (c) In terms of R, at...

Hi I'm trying to build a permanent magnet alternator with a different approach than usual. Most PMAs have a ring of magnets alternating north and south. But I'm wondering what would the field lines look like if ALL the magnets faced one direction? Would it provide a useful magnetic field, or...

Homework Statement f:A->A/I is a ring homomorphism. Does f^-1 take maximal ideas of A/I to maximal ideals of A?The Attempt at a Solution I think it does, since there is a bijection between A and A/I preserving subsets-ordering. But f might not be that bijection.

Why does Saturn's dust form a flat ring and not a sphere around it?

1. A point charge Q is held in the center of a charged ring. Half of the ring is charged uniformly with charge 2Q and the other half with 4Q. When the point charge is released, it accelerates toward infinitum. What is the ultimate speed of the point charge? 2. Homework Equations [E=F/q]...

Homework Statement A thin rubber ring of radius R lies in the xy-plane and is centered at the origin. The ring carries line charge density λ=λo*sin(Ø), with a constant λo with units C/m. define tan(Ø)=y/x. Calculate the magnitude and direction of the electric field E(z) created by the ring...

Homework Statement Hi guys, this question is from Kleppner and Kolenkow, problem 6.3. A ring of mass M and radius R lies on its side on a frictionless table. It is pivoted to the table at its rim. A bug of mass m walks around the ring with speed v, starting at the pivot. What is the...

There is a metal ball and a metal ring , through which the metal ball can pass easily. But when the metal ball is heated , it can't pass through the metal ring. What will happen if metal ring is heated?(keeping metal ball normal)

Homework Statement Homework Equations E=\frac{kqz}{(z^2+r^2)^{3/2}} The Attempt at a Solution (c) is asking where the maximum value of the electric field would be in terms of R. In order to do this, I have to take the derivative of this function, set it equal to zero, correct...

Homework Statement Determine both the location and the maximum magnitude Emax of the electric field along the axis of a uniformly charged ring. (Use epsilon_0 for ε0, Q, and a as necessary.) Homework Equations 1) dE= (ke)dq/r^2cos(theta) cos(theta)= x/r...

How fast are the electrons and the ions in the Ring Current (in the magnetosphere?)

Is it a huge daunting engineering task to create a very large dynamic o ring water seal (sliding up and down a shaft with ring on a mating surface) say about 50 or 100 meters in diamter? Would it be a good idea to make the ring and moving part a cube like shape so as to have a square seal...

I am very mystified by how piston and piston rings work (obviously they do). My questions are related but are in 3 parts: 1. What is highest pressure of the gas/liquid in a particular piston? (race car engine, construction machines...) and what is the approximate pressure in Kpa? 2. With...

Homework Statement A charge Q = - 710 nC is uniformly distributed on a ring of 2.4 m radius. A charge q = + 350 nC is placed at the center of the ring. Points A and B are located on the axis of the ring, as shown. In Figure below, an electron is projected along the axis of the ring from...