Ring Definition and 1000 Threads

I read that scalar matrices are the center of the ring of matrices. How would I prove this? Tips are appreciated. It is already obvious that scalar matrices commute with all matrices, but the converse seems tricky. BiP

Homework Statement I am suppose to find an expression for the electric field of a ring. Homework Equations E =\frac{Kq}{r^2} The Attempt at a Solution I calculated my results and I reached up to this: \frac{Kx\Delta q}{(R^2 + x^2)}^{3/2} where R = radius, x = distance, K =...

I am reading R.Y Sharp's book: "Steps in Commutative Algebra". On page 6 in 1.11 Lemma, we have the following: [see attachment] "Let S be a subring of the ring R, and let \Gamma be a subset of R. Then S[ \Gamma ] is defined as the intersection of all subrings of R which contain S and...

This is a question I gave in one of my exams. :D If $I$ is an ideal of the commutative ring $A$ (with unity), then prove that for each ideal $\overline J$ of the quotient ring $A/I$, exists an ideal $J$ of $A$ that contains the ideal $I$ and the lateral classes of $I$ defined by the elements of...

Hello folks! I've been trying to calculate the E-field of a charged ring. It seems well documented for a symetric point(a line from the center etc.) but what I'm interested in is say if I'm slightly of the center of the ring, how can I make a more general equation? I've tried calculating...

Homework Statement Suppose that a commutative ring R, with a unit, has no zero divisors. Does that necessarily imply that every nonzero element of R is invertible? Homework Equations The Attempt at a Solution We have to show that there exists some b in R such that ab = e. Having...

Homework Statement Assume a uniformly charged ring of radius R and charge Q produces an electric field Ering at a point P on its axis, at a distance x away from the center of the ring. Now the same charge Q is spread uniformly over a circular area the ring encloses, forming a flat disk of...

Magnet Phenomenon: The "divergent" region of a ring magnet Here's a puzzler: I have a NdFeB ring magnet, 1.75" outer diameter x 1.375" inner diameter x 0.25" thick, N40 grade. It is axially magnetized so that the north pole is toward one face and the south pole is toward the opposite face. The...

A ring on curved path (say on bent rod) will move longer distance than the one moves on straight line in same interval of time (the two rings are released simultaneously - one moves on curved path and other one moves horizontally) - How to explain? by which principle one can explain?

Homework Statement Hi, I'm trying to find the potential of conducting grounded sphere with radius Rs which located in the center of charged ring with Rr (>Rs) with charge density λ, h meters up to the z axis (see the attached images) Rs=4.3[cm] Rr=6.6[cm] h=13.1[cm] λ=1.0[esu/cm]...

hi every one on an exercise on book we ask us to find the electrical field for a uniformly charged ring where we going to find : E=kqz/(z2+R2)3/2 then we have to derivate it wth respect to z and we find : dE/dz=kq*(R2+2z2)/(z2+R2)5/2 so my question is how do we get this derivation ?

Homework Statement Homework Equations The Attempt at a Solution I started by calculating potential energy at a distance x(<<R). I used the approximation and differentiated the result to get an expression for force which came out to be F=-\frac{kQqx}{2R^3}\Rightarrow a=-\frac{kQqx}{2mR^3} This...

I was reading the following thread at stackexachange. http://physics.stackexchange.com/questions/9830/tension-in-a-curved-charged-wire-electrostatic-force-does-wire-thickness-mat The first answer calculates the radial force using the capacitance of ring. Any ideas how the poster derived the...

At which distance can you see Saturn's ring with a naked eye? I guess you would not be able to see it from Mars?

Hi... Having problen in understanding Newton's ring experiment ? And why are rings circular in shaoe ? Thanks in advance...:)

Homework Statement Consider the following ring: Considering that \theta = 30°, determine F1 and F2 in order for the net force to be oriented downards with magnitude 10^3 N and without any horizontal component. The Attempt at a Solution Alright, so, the problem is I find two conflicting...

Homework Statement A homogeneous ring lays horizontally on two identical parallel rails. The first rail moves parallel to itself, with a constant speed v; the second rail is at rest. The angular distance between the ring-rail contact points, as seen from the center of the ring, is 2α for the...

This work was motivated by the lack of open source analytic formulas for calculating the magnetic field of a current ring at any point in space As the result of the theoretical calculations, which are based on the law of "Bio Savart Laplace", the analytical formulas giving the ability to...

Let $$R=\mathbb{Z}[\sqrt{-13}]$$, let $$p$$ be a prime in $$\mathbb{N}$$, $$p\neq 2,13$$. Suppose that $$p$$ divides an integer of the form $$a^2+13b^2$$, with $$a,b$$ integers and coprime. Let $$P=(p,a+b\sqrt{-13})$$ be the ideal generated in $$R$$ by $$p$$ and $$a+b\sqrt{-13}$$ and let...

Hi there, I'm a university student and am stuck regarding a literature review for my individual project. I was given a schematic sketch of the setup of my experiment that showed a force acting on a hollow ring, and a strain gauges attached on the ring measured strain for the set force. I was...

I'm working on showing that Z3 is a ring. The one portion I'd like to confirm is the additive inverse part. So here's what I'm thinking as my proof: Given [x]3 , suppose [3-x]3 is the additive inverse in the set Z3 . Thus: [3-x]3 = [3]3 + [-x]3 = [0]3 + [-x]3 = [0-x]3 = [-x]3 Then, it...

Homework Statement [SIZE="4"]1. [SIZE="4"]2. Homework Equations ∫E.dA = Qenc/\epsilon_{o} \lambda=Q/L \rho=Q/V V= q/4πε_{o}r The Attempt at a Solution these types of problems i suck at, i don't know how to do these at all independently, and is there any difference in question 2 if there...

On page 273 of Dummit and Foote the last sentence reads: (see attachment - page 273) "The notion of the greatest common divisor of two elements (if it exists) can be made precise in general rings." (my emphasis) Then, the first sentence on page 274 reads as follows: (see attachment - page...

(Hungerford exercise 31, page 143) Let R be a commutative ring without identity and let a \in R Show that A = \{ ra + na \ | \ r \in R, n \in \mathbb{Z} \} is an ideal containing a and that every ideal containing a also contains A. (A is called the prinicipal ideal generated by a)

Hi guys: I have 3 questions: Imagine an open differential that looks like a gear ring : and now let's call the rings (orbital gear) the wheel gear, the gear in the center the center gear. 1. is the reason why torque from input shaft is evenly split to both wheels regardless...

Homework Statement I am going through the example problems in the book and it shows me how to find the electric field of a line of charge, which is this http://imageshack.us/a/img24/8932/img0303fq.jpg I get to this part where they change ΔQ to (Q/L)ΔY...

Homework Statement Let R be a ring with identity, and a,b are elements in R. If ab is a unit, and neither a nor b is a zero divisor, prove a and b are units. Homework Equations If ab is a unit then (ab)c=1=c(ab) for some c in R. The Attempt at a Solution Assume both a and b are...

Homework Statement A single large circular Olympic ring hangs freely at the lower end of a strong flexible rope firmly supported at the other end. Two identical small beads each of mass 30 kg are free to slide symmetrically without friction around the ring (the ring passes through the holes...

Homework Statement A ring of aluminum has a hole in the middle. When the ring is heated: a) the hole decreases in diameter b) the aluminum expands outward and the hole remains the same size. c) the area of the hole expands by the same percent as the area of the aluminum. d) the area of...

Homework Statement Is (x^2-1) a unit in F[x]? where F is a field. 2. The attempt at a solution I might say yes, cause we can find the taylor expansion of 1/(x^2-1), is my idea right?

Hi everyone, i have been looking at this problem for a few days now and i am pretty stuck, ill explain why first the problem : a charge Q is distributed over a ring section of radius r, between angles 90 and 180. find the V and E at the origin. Now the problem I am having ais everything...

What is the physical working principle of SRR's ? How do they result in the negative permeability at a macro level? (either of explanation or decent links will do!) Thanks :biggrin:

Homework Statement Consider the ring Z/mZ, show that S = {[0], [a], [2a], · · · , [m − a]} forms a (possibly nonunitary) subring of Z/mZ when a divides m. (i.e. show that (S,+, ·) is closed the usual addition and multiplication. (We are not require to find a multiplicative identity)...

I'm a little disappointed in myself for not being able to calculate this or find the answer online, but I've hit a bit of a mental block so I was hoping someone could help me out a bit. I was doing a thought experiment involving kerr-newmann black holes, and basically I would like to calculate...

Homework Statement The question : http://gyazo.com/5372336302b5ef289b305172bcd16a2a Homework Equations First Isomorphism theorem. The Attempt at a Solution Define \phi : \mathbb{Q}[x]/<x^2-2> → Q[ \sqrt{2} ] \space | \space \phi (f(x)) = f( \sqrt{2}) So showing phi is a homomorphism is...

Homework Statement A ring of radius 18 cm that lies in the yz plane carries positive charge of 5 µC uniformly distributed over its length. A particle of mass m that carries a charge of −5 µC executes small oscillations about the center of the ring on its axis with an angular frequency of...

Commutative ring, map R / ( I /\ J) -> ( R/I ) x ( R/J ) I quote an unsolved question posted in MHF (November 25th, 2012) by user needhelp2. P.S. Communicative note: Of course I meant in the title, commutative instead of communitative.

Homework Statement Two half-rings of charge of opposite polarity are brought together at the origin (so that the rings create a full circle against the y- and z-axis. Each half-ring has a charge of magnitude Q and radius a. Derive the net electric field at point P, located on the +x axis a...

Hello, I was wondering what the effect of gravity in a planet sized ring would be. If any of you have played the Halo game series, the ring structure is what I have in mind. -Would you be able to walk on the inside of the ring, and what forces will or will not permit you to? -Would you be...

I quote an unsolved problem posted in another forum on December 5th, 2012.

Homework Statement Didn't know what to title this one. I found it while I was doing some practice problems : http://gyazo.com/51a668d4db1a1638353a9de4b43d42ed Homework Equations lcm(m,n) = k for some integer k. The Attempt at a Solution I'm not really sure how to start this...

I have a question about the proof that I attached... 1) Since R/I is not the zero ring, we know that 1 \not= 0. What is the reason to say 1 + I \not= 0 + I instead of 1 \not= 0?2) Also, how do we compute something like (a+I)(b+I)? Isn't this correct (a+I)(b+I) = ab+aI+bI+I^2? 3) Finally, if we...

Homework Statement If R is a domain with F=Frac(R), prove that Frac(R[x]) is isomorphic to F(x). Homework Equations The Attempt at a Solution Let \phi : Frac(R[x]) \rightarrow F(x) be a map sending (f(x),g(x)) to f(x)/g(x). We need to show that \phi is a ring homomorphism. Let f,g,h,k be in...

Homework Statement This is the diagram http://s1302.beta.photobucket.com/user/Rameel17/media/dd_zps43d04d44.png.html A single large circular Olympic ring hangs freely at the lower end of a strong flexible ring which is firmly supported at the other end. Two identical beads each has a mass...

I attached a page from my textbook, because there was something that I didn't understand. What I don't understand is in the proof it says let f(x) be...etc. but in the theorem, it says nothing about f(x). In other words, where in the thoerem does it say anything about f(x). Why are they...

Hey! Is there an infinite ring with exactly two maximal ideals. Thanks in advance LiKeMath

I've just got confused about how the induced current in a metallic ring is calculated. Consider a metallic ring (radius a, resistance R and inductance L) immersed in a oscillating magnetic field, which is oriented orthogonally to the plane of the ring. The variation in flux of magnetic...

Hi! I aim to use a piezoelectric wafer and get it to work as a loudspeaker by supplying it with a fluctuating voltage withing the audible region. I know this can be done using a simple DC to AC invertor/oscillator circuit, but the challenge is to build it as small as possible. I looked up...

Homework Statement Apply the physical pendulum equation to a ring pivoted on its edge to derive the equation for the period of a ring pendulum for small oscillations about the pivot point. Include a diagram showing the restoring torque acting on a ring pendulum displaced from equilibrium...

Good afternoon. Here is the problem: Show that if $R$ is a ring with unity and $N$ is an ideal of $R$ such that $N \neq R$, then $R/N$ is a ring with unity. My answer: Consider the homomorphism $\phi: R \to R/N$. Given $r \in R$ we have that $\phi(r) = r + N = \phi(1 \cdot r) = \phi(r \cdot 1)...