Ring Definition and 1000 Threads

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...

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...

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...

how to calculate induced emf in split ring resonator SRR of Metamaterial. what are the values of inductance capacitance & resistance of SRR

Suppose we let R be a commutative ring with identity, and let I be any ideal of R. And we define the RADICAL of I to be the set N(I) = {r \in R: r^n \in I for some positive integer n}. I need the proof that: If I contains a unit of R, then show that I = R. N(N(I))=N(I) An...

Has anyone heard of a permanent magnet in the shape of a ring or toroid with no poles? I believe that one could be made by winding a ring of magnetic material, such as steel, with a wire winding, like one winding of a toroidal transformer. DC current could then be passed through the winding...

The teenager, Ariana Iacono, belongs to the Church of Body Modification. Should "religious" items of clothing and jewelry be forbidden in non-parochial schools? http://news.yahoo.com/s/ap/us_rel_piercing_church

Homework Statement A thin ring of mass M and radius R rotates around its vertical axis. A small ball of mass m can slide, without constraint nor friction, on the ring. If the angular speed of the ring when the ball is at the top is [\tex]\omega_0[\tex], what is the angular speed when the ball...

Homework Statement I need to find the inverse to element in 7 in ring Z_{13} Homework Equations 7^-1 in Z_{13} The Attempt at a Solution Needs to find X so that, 7x=1 in Z_{13} => 7x=1+k*13 And then my notes was messed up :(

Homework Statement "A round plug made of brass has a diameter of 87.53 mm at 20 C. The plug is to be fitted to a steel ring of inside diameter 87.43 mm. To what common temperature must they be brought in order to fit?" The linear coefficient of expansion for brass: \alpha_{b} = 18.7 \cdot...

Homework Statement A thin, circular ring of inner radius a and outer radius b carries a uniform surface charge density \sigma (i) Find an expression for E at a point on an axis perpendicular to the plane of the disk, the axis passes through the centre of the disk. (ii) Keeping the surface...

What caused the ring around the atomic mushroom in Nagasaki?

Homework Statement Using only the ring axioms, prove that in a general ring (R, +,X) aX (x-z) = (aXx)- (aXz) where all a,x,z are elements of R Homework Equations Group axiom 3: G3= There is an inverse for each element g^-1 *g =e Ring axiom 3: R3= Two distributive laws...

Hello everyone I am trying to simulate a three phase AC powered six coil stator ring using Multisim or Orcad. How would I do this? Would I use regular inductors as the coils or would I use coils with iron and steel rods inside them? Would I just connect each inductor coil pole pair...

Hello. I got this question, it pursues me in my sleep lately. What will happen with a superconducting ring, passed through magnetic field? I mean like will the electrons even flow in it, taking that magnetic field is banned out of the material? And if they flow will the ring need extra force...

If you think of a sphereical symmetric diffraction ring, the intensity is constant for each sphereical section (intensity doesn't vary for theta or phi), but it varies kind of like a sine wave in the r dimension from zero to zero with a maximum in the middle of the ring. So that if you think...

Hello everyone: I am trying to find a program or formula that will help me figure out how many windings, turns of coil, are needed per coil on a 6 coil steel stator ring powered by 3-phase AC power to get a certain magnetic field strength, about 1.3T. Is there any way that you could help me...

Hello everyone: I am trying to find a program or formula that will help me figure out how many windings, turns of coil, are needed per coil on a 6 coil steel stator ring powered by 3-phase AC power to get a certain magnetic field strength, about 1.3T. Is there any way that you could help me...

Suppose we have a necklace made of a conducting material. We join the two ends and leave it on a frictionless non-conducting table. Then we charge it negatively. What is the equilibrium shape of the necklace? The answer to this is probably a circle. I am actually looking for the differential...

Let R be a ring . Suppose that e and f=1-e are two idempotent elements of R and we have R=eRe \oplus fRf (direct sum ) and R doesn't have any non-trivial nilpotent element . Set R_1=eRe and R_2=fRf . If R_1=\{0,e\} and R_2 is a local ring , then prove that R_2 is a division ring . (note that e...

Can anyone give an example of a ring homomorphism f : R -> R', such that R is a integral domain but the Image(f) is not an integral domain. I was thinking that since we want two non zero elements of Image(f) multiply to 0, we require: f(xy) = f(x)f(y) = 0, with f(x), f(y) not 0. Now f(xy) =...

Hello all, I am currently working on a project that requires a stator ring like the ones found in electric motors where there are 2-3phases of electromagnetic coils placed in a circular fashion with a pole pointing towards the center (look at picture below). The coils would be powered by AC...

Homework Statement I have a ring, radius a, with a charge distributed evenly around it. Using a gaussian cylinder of radius r, r<<a (or otherwise). Find the electric field at at small distance r away from the centre of the ring, r is in the plane of the ring. I know that the answer is...

Homework Statement A ring of radius a has a charge distribution on it that varies as \lambda(\theta) = \lambda_{0}sin \theta. a.) What is the direction of the electric field at the center of the ring? b.) What is the magnitude of the field at the center of the ring? The textbook...

Hello all, I am currently working on a project that requires a stator ring like the ones found in electric motors where there are 2-3phases of electromagnetic coils placed in a circular fashion with a pole pointing towards the center (look at picture below). The coils would be powered by AC...

Homework Statement A long bar magnet is bent into the form of a closed ring. If the intensity of magnetisation is M, and ignoring any end effects due to the join, find the magnetic field H and the induction B: (a) Inside the material of the magnet (b) just outside Homework Equations...

Homework Statement how that N is a maximal ideal in a ring R if and only if R/N is a simple ring. that is it is nontrivial and has no proper nontrivial ideals. Homework Equations The Attempt at a Solution I don't know how to start. Please help.

Homework Statement give an example to show that a factor ring of a ring with divisors of 0 may be an integral domain. Homework Equations since we know that ZxZ is a zero divisor and 5Z is an integral domain. The Attempt at a Solution So, ZxZ/5Z =~(isomorphic to) Z/5Z=~ Z_5.

Homework Statement Given a commutative ring with unity, show that if every ideal is prime than the ring is a field. Homework Equations The Attempt at a Solution I think that I can show that a ring is a field iff it has no nontrivial ideals. So I guess I need to show that if a...