Ring Definition and 1000 Threads

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).

[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

Consider a mass m confined to a ring of radius r. The potential everywhere on the ring is zero. In the ml = +3 state, identify the points on the ring where the probability of the particle existing is zero. I was thinking that every point would be zero, because it's a wave, not a particle...

Homework Statement A circular ring of charge of radius b has a total charge q uniformly distributed around it. The magnitude of the electric field at the center of the ring is: [Answer: 0] Homework Equations The Attempt at a Solution From the problem, do you just assume that the...

Homework Statement A metal ring 4.6 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...

Homework Statement Show that the quaternion division ring H has infinitely many u satisfying u^{2}=-1 Homework Equations Elements of H is of the form a.1 +bi+cj+dk where a, b, c, d in \textsl{R} ( reals) and i^{2}= j^{2}= k^{2}=ijk = -1. The Attempt at a Solution Let u = a.1...

The New York Governor, Eliot Spitzer (D) has been linked to a prostitution ring as reported in the New York Times (and thus it could all be a big lie). As attorney general in 2003, Spitzer http://www.nytimes.com/2008/03/10/nyregion/10cnd-spitzer.html?_r=1&hp&oref=slogin It seems very unlike...

I have troubles to do this one problem dealing with particle-on-a-ring, Suppose we have a wavefunction as, g(phi) = cos(phi) + 2 sin(2phi) First, normalize the function g(phi). By inspection, or otherwise, write g(phi) as a linear combination of eigenfunction of Lz. State what possible...

I was searching for the definition of localization of a ring . I came across the definition given at http://mathworld.wolfram.com/Localization.html If i take S as an ideal, the requirement 1€S make S=R. I am confused here how can i define localization of a ring at an ideal.

[SOLVED] Voltage from Ring of Charge Homework Statement A plastic rod has been bent into a circle of radius R = 6.40 cm. It has a charge Q1 = +2.40 pC uniformly distributed along one-quarter of its circumference and a charge Q2 = -6Q1 uniformly distributed along the rest of the circumference...

1. Consider the set Z of integers, and let R denote the subset all multiples of 4. Define addition as ordinary addition in Z, and define multiplication * in R by a*b = ab/4 a. Show that (R, +, *) is a ring with unity (what is the unity of R?) b. Show that the mapping Ø: R → Z defined...

Homework Statement Can someone explain the notation of the integer ring(Z)? My friend's in Math 100 and has questions on Z. I have never heard of ring's before and I'm at a loss to help him. From what I've gathered Z is a set of all integers. They ask for the invertible elements in different...

1. [B]The problem statement Let R be a ring. The center of R is defines as follows: Z(R)= {x E R where xy = yx for all y E R} Show that Z(R) is a subring of R The Attempt at a Solution I know that rings have to follow 4 axioms a) its an abelian group under addition b)...

I'm having a problem finding and equation that will give me the tensile stress acting on a spinning ring, like the rim of a flywheel, that is trying to "pull itself apart". The ring has no spokes or disc, but is just a ring spinning on its axis. I need to know how fast the ring can spin...

Homework Statement Three electrons are confined to move on a ring of radius R. Find the equilibrium positions of the electrons in terms of the angles between them. Homework Equations Some hints with differentials are given to us, as is the potential between two of the electrons , but as...

So the problem is: "4:(a) Determine the prime ideals of the polynomial ring C[x, y] in two variables." "We recognize that an ideal P is prime if and only if for two ideals A and B, AB $\in$ P implies that either A or B is contained in P. So we must find " So anyways, I'm thinking that it...

[SOLVED] show a matrix ring is simple Homework Statement Show that the matrix ring M_2(Z_2) is a simple ring; that is, M_2(Z_2) has no proper nontrivial ideals. In my book M_2(Z_2) is the ring of 2 by 2 matrices whose elements are in Z_2. Homework Equations The Attempt at a...

Homework Statement Let R and R' are rings and phi: R to R' is a ring homomorphism such that phi[R] is not identically 0'. Show that if R has unity 1 and R' has no 0 divisors, then phi(1) is a unity for R'.Homework Equations The Attempt at a Solution Its relatively obviously why phi(1) has to...

[SOLVED] ring theory question Homework Statement My book says that "if a is an integer relatively prime to n, then the coset a +nZ of nZ containing contains an integer b < n and relatively prime to n." If 0< a < n, this is obvious. If a > n or 0 > a, I do not see why that statement is...

[SOLVED] ring theory problem Homework Statement True or false. The product of two nonunits in Z_n may be a unit. Homework Equations The Attempt at a Solution If a and b are two non units in Z_n, and ab <= n, then the result is clear, since ab would not be relatively prime to n...

Homework Statement Let R be a ring that contains at least two elements. Suppose for each nonzero a in R, there exists a unique b in R such that aba=a. Show that R has no divisors of 0. Homework Equations The Attempt at a Solution Let a*c=0 where a,c are not equal to 0. aba=a...

[SOLVED] Electric Field Produced by a Ring 1. Homework Statement A uniform circular ring of charge Q=5.60microCoulombs and radius R=1.30 cm is located in the x-y plane, centered on the origin as shown in the figure. If z is much smaller than R then E is proportional to z. (You should...

Let a and b belong to a commutative ring R. Prove that { x ∈ R | ax∈bR } is an ideal. i really need help thx

The problem: You are part of a design team assigned the task of making an electronic oscillator that will be the timing mechanism of a micro-machine. You start by trying to understand a simple model, which is an electron moving along an axis through the center and perpendicular to the plane of...

Homework Statement Show that the intersection of any two subrings of a ring is a subring. The Attempt at a Solution It seems abstract. suppose a+b=c and a*b=d Then if c is in A and B (where A and B are subrings) then the intersection of A and B denoted by C contains c and if C...

Hey everyone, I was hoping to grab some quick advice on these two topics. Specifically, I'm a 4th year physics undergrad with all the standard physics and math courses, as well as real analysis up to lebesgue measure theory/integration theory+hilbert spaces,etc., and grad level PDEs. I...

Homework Statement Show that x^2 +3*x+2 has four zeros in Z(subscript 6), Homework Equations The Attempt at a Solution x^2+3*x+2=(x+1)(x+2)=0=>x=2, and x=1 6*1=6 3*2=6 according to the back of my textbook , the other two zeroes for x^2+3*x+2 are x=4 and x=5. is it...

Dear all, Can only the outter planet form rings? If Saturn were moved very close to the Sun, would it be able to maintain its ring system? I personally don't think so due to the fact the high tmperatures would vaporise a lot of the ice in the ring system but I would like to everyone else's...

Homework Statement Consider a thin ring of radius a and mass M. A mass m is placed in the plane of the ring (not in the center!). Determine the gravitational potential for r < a. Find a position of equilibrium and determine whether it is stable or unstable. (Hint: Consider a small...

Does there exist a solid concrete detailed textbook on Ring Theory? I'm looking for something like Rotman's book of Group Theory. My background consists of basic Ring Theory/Field Theory from Herstein's Abstract Algebra. I have Rowen's book in my hands right now (library), but it's far...

Hi as the title says i´m looking for an example of a ring witch has only one sided inverses e.g left or right sided ones -> a*b=1 does not imply b*a =1! thanks for your advice :)

Homework Statement If A is an ideal of a ring R and 1 belongs to A, prove that A=R. Homework Equations The Attempt at a Solution I said that r should an element of R. and since A is ideal to ring R and 1 is an element of A , then ar should be an element of A . 1 must be an...

I'm having trouble solving this question... If the epsilon ring of Uranus is 75 km wide, how long will it occult a star? Any help would be greatly appreciated.

The problem statement: Determine the maximum electric field on the axis of a ring of charge 4.3mC. The radius is 4cm. I think the key is to use ekvation 1 and derivate to determine the maximum electric field but I'm not sure. Q is the charge, x is axis of the ring, a is the radius. Any...

Hello condensed matter gurus out there, I'm a new graduate student who's been trying to understand some sentences in a review article that reads: ----- ... One of Feynman's early successes with path integrals is often neglected, his mapping with path integrals of a quantum system onto a...

Homework Statement Let R be a commutative ring and a,b in R. Show that the canonical image of ab in R/(f - f^2*g) is idempotent. Give an example where this idempotent is not 0 or 1. Homework Equations None. The Attempt at a Solution Well I've tried playing with the properties of...

Say I have x^2 + 1 = 0 mod 7, it is clear that adding a linear polynomial congruent to 0 will give away the solution; problem is, what polynomial is that? Trial and error is quite tedious, though I doubt it, is there a direct way?

I'm going through this proof in Allan Clark's Elements of Abstract Algebra to prove that a primigenial ring is a Dedekind Domain. A primigenial ring is one in which every proper ideal can be written as a product of proper prime ideals. There's a step in the proof that I'm not able to...

If I have a charged insulating hula-hoop with the property that every point on the ring has exactly the same charge per volume as every other point on the ring, and I spin it around its axis, does that produce a current? If I consider a "window" cutting through some part of the ring, I will see...

Homework Statement Problem from Fluid Mechanics (Streeter, McGraw Hill, 9th ed.) 1.70 A method used to calculate surface tension of a liquid is finding the force necessary to pull a platinum ring out of the surface of that liquid. Calculate the force necessary to pull a ring with a 20mm...

Homework Statement A ring of radius 'a' has a charge distribution on it that varies as \lambda (\theta) = \lambda_0 sin(\theta), where \theta is the angle between 'a' and the x axis. a) What is the direction of the electric field at the center of the ring? b) What is the magnitude of...

Hi guys. I was wondering if any of you happened to know the equation for the radial and tangential stress developed across a segment of a ring in rotation. I have been looking through countless machine element design books, and all I can come across is one for a solid ring (like a flywheel)...

Hi everyone. I have two questions that I hope you can help me with. First when trying to show isomorphism between groups is it enough to show that the order of each element within the group is the same in the other group? For example the groups (Z/14Z)* and (Z/9Z)*. They are both of order...

I don´t know how to solve it. Thanks beforehand

Hey First off, my terminology in the title may not be correct or what others use because when searching the forums for "polynomial ring" i had a lot of trouble finding anything that matched what i meant when i coined the term... By polynomial ring i mean, for some ring R the polynomial...

Hello all. I am in need of a quick clarification. A text I am reading describes an ideal in a ring as 'analogous' to a normal subgroup of a group but there appears to be a slight difference in structure in that a member of the underlying additive group from which the ideal is formed operates...