Ring Definition and 1000 Threads

I need to find all the ring homomorphisms of f:Z[sqrt(2)]->Z 7 basically I don't even know where to start. any suggestions would be great

1. Problem1 statement, all variables and given/known data In the figure particle 1 of charge q1 = -8.13q and particle 2 of charge q2 = +3.63q are fixed to an x axis. As a multiple of distance L, at what coordinate on the axis is the net electric field of the particles zero...

Is there a strength and/or field density difference between ring and disk magnets? I want to know which would create stronger eddy currents when dropped through a copper tube (which one would fall slower).

The Einstein cross (G2237+030) shows 4 reasonably symmetrically spaced images of the very distant quasar, indicating that our alignment with the galactic nucleus to quasar line is fairly good. How is that it does not show an Einstein ring instead of the cross?

Homework Statement Take the ideal I = < 6, 3 + 3 \sqrt{-17} > in the ring Z [ \sqrt{-17} ]. Determine whether this ideal is prime or not. Homework Equations <18> = I^2 There is no element \alpha \in Z [ \sqrt{-17} ] such that 18 = \alpha^2 The Attempt at a Solution...

I'm having trouble with what seemed like a trivial problem at first, but now I'm rather stuck. If R is a ring with xy=-yx for any x,y from the ring, xyz+xyz=0 must be true for any x,y,z from the ring. I'm trying to show why that is. Letting y=x yields x^2+x^2=0. Thus then breaking it up into...

I know that Z/(p) that is the integers mod a prime ideal is a field and I also know that: Field -> Euclidean Domain -> Principal Ideal domain -> Unique factorization domain ->Domain So I know that Z/(p) are all of these things. I also know that Z/(a) That is the set of integers mod a non...

My teacher put heavy emphases on acknowledging that a subset is nonempty of a ring when proving something is a subring of something. For the final exam, she wants to put a question with empty subset of a ring, and do subring proof. The empty subset would have "nice" description so you can do...

What is the definition of a characteristic of a ring? Is it the smallest n such that n1=0? or is it the smallest n such that nr=0 for all r in R.

How can i find the electric field due to a charged ring off-axis? Actually i have two ring electrodes in parallel and i would like to know how to find the electric field at any point in between the ring electrodes?

Homework Statement Aut(R) denotes the set of ring automorphisms of a ring R Show formally that Aut(R) is a group under composition. Homework Equations The Attempt at a Solution I Have a very similar question to which I have the solution viz Aut(G) denotes the set of group...

I am trying to built a double ring electrodynamic trap for aerosol particles. Please suggest me for this project. Thanks

Homework Statement How do I determine the normalization constant, N for a particle on a ring with wave function Ψ= Ne^(imφ) ? Homework Equations The Attempt at a Solution

Suppose two cooper rings,each having the same surface smoothness and of same size(geometry).The only difference is that interior of the first ring is hollow while of the second isn't.m1<<m2. If we send two rings,with same inital velocities,to glide across a frozen long path of ice,which one...

So right now I'm trying to solve this problem in ring theory for homework. The question pertains to proving that in a PID, D, if a,b are elements of D then the gcd of a and b can be written as a linear combination. In any event I know where I have to go but I'm stuck on this one bit of notation...

Definiton If a and b are two nonzero elements of a ring R such that ab=0 then a and b are divisors of 0 or (0 divisors). In particular a is a left divisor of 0 and b is a right divisor of 0. My question is if you have a0=0 then a is not a 0 divisor? So it seems that 0 divisors will...

Homework Statement I have the field at the center of a charged ring on the x,y axes (top half has charge density of -lambda, bottom is +lambda lambda=la) to be E=(lay^)/(2pi epsR) (eps=epsilon) i can't find the potential for this, R=radius, Can anyone help? Homework Equations...

Homework Statement How do I find the electric field from a semi-ring of charge at the center of the would-be circle? Does that make sense? Or another way: If the semi-circle of charge is centered at the origin, what is the electric field at the origin? I hope you know what I mean now. the...

hi, this is my first post here in this forum. i would like somebody here to help me in calculating the force exerted onto the pipe by a stainless steel ring of 10mm thickness, when it is shrunk fit on to the pipe by heating. thanks in advance

Hi, I'm having some difficulty predicting favourable rearrangements in alicyclic carbocations. When, why and how does a ring in a carbocation expand? I've seen some drawings (not sure whether they are correct though) where tertiary carbocations undergo ring expansion to a secondary...

ok here goes, A uniformly charged ring has a radius equal to 10.0cm and a total charge of +12.0nC. An electron is placed on the ring's axis at a distance of 25.0cm from the center of the ring and is constrained to stay on the axis of the ring. The electron when it reaches the center of the...

While I'm on the topic, here is another ring I need to show Euclidean. I'll show more of the work this time too. The ring is Z[{\sqrt 2 \over 2}(1+i)] So, using the standard norm difference approach, we pick any element alpha in the field and try and show we can always find an element beta in...

Let \displaystyle{\zeta = e^{{2\pi i} \over 5}} I need to show that Z[\zeta] is a Euclidean ring. The only useful technique I know about is showing that given an element \epsilon \in Q(\zeta) we can always find \beta \in Z[\zeta] such that N(\epsilon - \beta) < 1 (using the standard norm for...

I just need confirmation. I have a problem in my algebra class that says: Prove that there are no ring homomorphisms from Z5 to Z7. I have the following definition of ring homomorphism: Let R and S be rings. A function R to S is a ring homomorphism if the following holds: f(1R)=1S...

"Atlantean ring" (talisman) Have anyone heard about this "wonderful" talisman?, :confused: :confused: according to webpages and internet, can provide you "prosperity and luck", :!) :!) they're sellling just for 40 €€ but i don't know if there are some "scam" about it what's your opinion :mad...

Hello All, I was talking to one of my EE friends and they were telling me about this thing called a ring oscillator which could oscillate by itself simply by connecting a bunch of diodes in a loop. I was just wondering if someone could give me more information about this. I'm specifically...

To make a long story short, the problem has an elliptical ring from width E to E+dE in phase space (p on y axis, x on x axis). This is a harmonic oscillator, so the standard equations apply (E=p^2/2m + kx^2/2)... now for the question I need to find the total area in the ring of the ellipse in a...

a ring of mass M hangs from a thread, and two beads of mass m slide on it without friction. the beads are released simultaneously from the top of the ring and slide down opposite sides. show that the ring will start to rise if m>3M/2, and find the angle at which this occurs. what i did: i...

I've been stuck on this problem for awhile now.. At what distance along the central axis of a ring of radius R and uniform charge is the magnitude of the electric field due to the ring's charge maximum? Now, I know that the equation for this problem is E = [k|qz|] / [(z^2+R^2)^3/2], which...

Can you hear it? I can't. My ears are too old. :frown: http://www.freemosquitoringtone.com/offer.asp?gclid=COHXudCry4UCFU1dDgodVAWW2w *warning - just in case you don't read further than this post, a few people have mentioned later in this thread that this tone is actually painful*

Let S be a ring such that for all s in S, s2 = s. Prove that S is commutative. I've proved that for all s and t in S, (s + t)2 = s2 + t2, and also that s + s = 0. How would I go about proving that for all s and t, st = ts? Thanks. By the way, this isn't exactly homework, I was just...

Sir, The diameter of a metal ring is D and the coefficient of linear expansion is y. The temperature of the ring is increased by 1 degree Celsius. What is the increase in area of the ring? I solved it the following way: Coefficient of superficial expansion = 2y Initial area of the...

If R is a ring, and has the property that x^3=x for all x in R, then show R is commutative. Generalize for x^k=x, k an integer >3. I can do this for x^2=x. First use x^2+x^2=x+x=(x+x)^2 = 4x^2 (abusing notation a little) which means x^2+x^2=x+x=0, ie, x=-x for all x in R. Then...

An aluminum ring of radius 5 cm and resistance 0.003 ohms is placed around the center of a long air-core solenoid with 1000 turns per meter and a smaller radius of 3 cm. If the current in the solenoid is increasing at a constant rate of 270 A/s, what is the induced current in the ring? B=...

Consider the ideal I of Q[x] generated by the two polynomials f = x^2+1 and g=x^6+x^3+x+1 a) find h in Q[x] such that I=<h> b) find two polynomials s, t in Q[x] such that h=sf+tg

I'm currently stuck on this question on the image attachment. Any help would be definitely ppreciated. Ok, so from what I understand, it asks what is the current that passes through the fixed line. For part (a), I see that the current is 'discontinuous', and I'm not enitrely sure how to solve...

Is a ring accelerator the same as a cyclotron? If not can someone please tell me somthing about ring accelerator, or send me links where I can find some information about ring accelerators.

Let g(x)\in F[x], T\in L(V). Let F[T] be a ring generated by g(T). Show that if g(T) is invertible, then g^{-1}(T)\in F[T]. No idea what do do.

I am trying to calculate the current induced in a loop assuming a magnetic monopole exists. The loop is a perfect conductor, which I understand implies the electric field inside must be zero. I picture the problem with the magnetic monopole traveling with a velocity coaxial with the loop. I am...

I'm searching for some online text concerning an introduction and somewhat more advanced topics in ring theory. ps:if you come across on notes for Model theory it would be great too,thx.

This needs to be done with Coulomb's Law: A ring of radius R has a charge distribution on it that goes as \lambda (\theta)= \lambda_0 sin \theta as shown in the figure below: http://img506.imageshack.us/img506/8898/naamloos2iz.th.gif In what direction does the field at the center of...

i have a few problems that i was struggling with. Projectile motion: An electron is fired in an electric field E=-720j. Its launched with a velocity of 9550 m/s. if you want the x distance it travels to be 1.27mm, what are the two values of theta that will work? how long does it take...

Just came out, with every minute of music from the film on disc (three full hours of score). This is great. I have to go now. Gandalf just fell to the Balrog and I need a moment with the hobbits (for pity's sake!). http://www.lordoftherings-soundtrack.com/

I am stuck on this problem: I started this problem by looking at the electric potential of a ring, which is: V=\frac{kQ}{\sqrt{R^2+z^2}} So then if it varies in the thickness of the ring, would it be reasonable to have it be: V=\frac{kQ}{\sqrt{(R_{out}-R_{in})^2+z^2}} Or would I...

A very intelligent, humorous, wise and handsome guy with a degree in anything (preferably not physics and art), who would buy me this http://www.ashford.com/product/index.asp?sn=458045054&md_id=1&pf_id=40646&dept_id=60&comp=Y on Valentine's day! :blushing: Intelligent: IQ > 150 Handsome...

I have been doing some thinking about the collapse process inside a rotating black hole. (I think that the probability of creating a non rotating black hole with its point singularity and awkward infinities is so unlikely as to be not worth bothering about). Note this analysis requires no new...

A 25.5 g silver ring (Cp = 234 J/kg times degrees C) is heating to a temperature of 84 degrees C and then placed in a calorimeter containing 5 x 10 to the negative 2 power kg of water at 24 degrees C. the calorimeter is not perfectly insulated, however, a 0.140 kJ of energy is transferred to...

How does one compute the number of ring homomorphisms from \mathbb{Z}_2^n to \mathbb{Z}_2^m? Or, likewise, the number of linear mappings on those two vector spaces?

Does bromobenzene mean that a bromine is bonded to every carbon in the benzene ring? When it saids 1-ethylbenzene where do i put the ethyl since benzene is in a ring? Thx in advance

Happy New Year! Yay! Its going to be the new year in about 5 hours and 10 minutes for me. Happy NEW YEAR fellow PFers!