Ring Definition and 1000 Threads

Let R be an ordered Ring. Assume R+ is well-ordered Prove: a) min(R+) = 1. b) R is an integer ring

Let R be a non-commutative ring . Suppose that the number of non-units of R is finite . Can we say that R is a finite ring?

Homework Statement Show that a+b = b+a follows from the other ring axioms. Homework Equations a + 0 = 0 + a = a (?) The Attempt at a Solution I know this is probably a simple algebraic manipulation, probably with the distributive law, but I don't know how to start! I'm sure I need...

Homework Statement Problem 3.5.2 Let R be a ring such that the only right ideals of R are (0) and R. Prove that either R is a division ring or that R is ring with a prime number of elements in which ab = 0 for every a, b \in R. Homework Equations The Attempt at a Solution...

1. Homework Statement Derive and show that the period for a thick ring would be T=2π√[d/g+(ΔR)^2/4Rg] 2. Homework Equations "the ring pendulum consists of a thin metal ring that can be suspended from a knife edge. The ring has inner radius Ri and outer radius Ro. A notch is cut...

Let R be a ring with multiplicative identity 1R. Suppose that R is finite. The elemets xy1, xy2,...xyn are all different. So x y_i=1R for some i. A lemma that is not proven is given. If xyi=1R & yjx=1R, then yi=yj I need to show that yjx=1R. Right now I haven't got much. I took...

Homework Statement Proof that there is no ring homomorphism between M2(R) [2x2 matrices with real elements] and R2 (normal 2-dimensional real plane). Homework Equations -- The Attempt at a Solution I have tried to proof this problem with properties of ring homomorphism (or finding...

Can anyone explain, in detail, why/why not Z[X]/(2x) is isomorphic to Z/2Z? I know that every element in Z[x] can be written as a_0 + a_1 x + a_2 x^2 + ... with a_i in Z and only finitely many a_i's are nonzero. Now, does (2x) = (2, 2x, 2x^2,...)? Also, the quotient is "like" taking 2x=0, or...

the problem is stated as The Earth’s magnetic field at a certain location in the UK has a magnitude of 48 μT and is directed at 66° below the horizontal. a)Determine the magnitude of the flux of the Earth’s magnetic field through a wedding ring of diameter 2.2 cm when the ring is held in a...

Homework Statement the molecular formula of the compound under analysis is C8H8O2 = Mr of 136 the mass spectrum shows the peak at 91 to be the most stable. I'm supposed to obtain structures representing the peak at 91 as well as at 118 and 65 The Attempt at a Solution I represented 91...

Let R be a commutative ring with unity. I and J are ideals of R. Show that If I + J = R, then I∩J=IJ. I know that IJ⊆(I∩J). But I can't do inverse.

I was in the French Alps the other day, high in the mountains (not sure if this is relevant), and, on the night of a full moon, with mist in the sky, there was a circular ring of light around the moon. The ring subtended an angle about 5 times that subtended by the moon (that is to say, it...

let R be a non-commutative ring and D(R) denotes the set of zero-divisors of the ring . Suppose that z^{2} =0 for any z \in D(R) . prove that D(R) is an ideal of R.

Let R be a ring with 1_R. If M is an R-module that is NOT unitary then for some m \in M, Rm = 0. I'm pretty sure Rm = \{ r \cdot m \mid r \in R \}. While M being not unitary means that 1_R \cdot x \neq x for some x \in M. I'm thinking this problem should be an obvious and direct proof but I...

let R be a matrix ring over a finite field \LARGE F_{q} , i.e. \Large R=M_{n}(\LARGE F_{q}). then 1.Every matrix of rank n-1 in any maximal left ideal generates the maximal left ideal. 2.moreover,the number of matrices in every maximal left ideal that can be a generator is the same as the...

1) R is an integral domain and P is a prime ideal. Show R\P (R complement P or R-P) is a multiplicative set. -Well since R is an integral domain it contains 1. -{0} would be a prime ideal, and that was removed (is this too much to assume) I'm not sure how to show multiplication is...

Homework Statement Consider a charged ring of radius 20.6 cm and total charge 12 nC. We are interested in the electric field a perpendicular distance z away from the center of the ring. At what distance from the center of the ring does the electric field become maximum? Hint: The...

hi guys, just want to ask, an open loop has three points A,B, C and each point serving a load. there is only one source (a subtransmission 69kV line from a substation), connected at point A. The loop is open at line segment AC (the circuit breaker at point C, connecting the segment AC is...

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 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...

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...