Ring Definition and 1000 Threads

I am reading T. S. Blyth's book "Module Theory: An Approach to Linear Algebra" ... ... and am currently focussed on Chapter 1: Modules, Vector Spaces and Algebras ... ... I need help with an aspect of Theorem 1.1 part 4 ... Theorem 1.1 in Blyth reads as follows:In the above text, in part 4 of...

Hi, can someone explain me the next experiment: If I have an AC coil on iron stick, and if I put Cu ring on that stick concentric with AC coil, when I turn coil power supply, the ring will levitate on some height. My question is: Powered AC coil produces an AC magnetic field. If I put a...

Hello! I'm completely new to working with arduino and electronics and am currently working on a little project involving a stepper motor. I need to be able to detect in which direction the motor is pointing. In order to do so, I came up with an idea inspired by how potentiometers work. The idea...

what is Ring Main Unit design in electrical panels ?

Hey there, I need some help with this assignment: Use the definition for a ring to prove that Z7 is a ring under the operations + and x as defined as follows: [a]7+[b]7 = [a+b]7 and [a]7 x [b]7 = [a x b]7 1. state each step of your proof 2. provide written justification for each step.But...

On page 284 Dummit and Foote in their book Abstract Algebra define a prime element in an integral domain ... as follows: My question is as follows: What is the definition of a prime element in a ring that is not an integral domain ... does D&F's definition imply that prime elements cannot exist...

On page 284 Dummit and Foote in their book Abstract Algebra define a prime element in an integral domain ... as follows:My question is as follows: What is the definition of a prime element in a ring that is not an integral domain ... does D&F's definition imply that prime elements cannot exist...

If I get a pack of 1,000 jump rings (for jewelry), and the bag costs me $8, how much is EACH jump ring? is it 8 divided by 1,000, which is .008 cents per ring, or is this .008 dollars, and I move the decimal spaces two to the left to get cents? I m a bit confused... Thanks!

Homework Statement [/B] Thin rod of length l is placed with one of its ends at the center O of the (thin circular )ring of radius R as shown (Figure 1), perpendicular to the plane of the ring. The rod is charged with total charge Q that is distrubted along the rod's length with linear charge...

Hey! :o Let $R$ be a commutative ring with unit and $M$ be a $R$-module. I want to show that the endomorphism ring $\text{End}_R(M)=\text{Hom}_R(M,M)$ of a simple $R$-module is a field. We have that $\text{End}_R(M)=\text{Hom}_R(M,M)=\{f:M\rightarrow M \mid f \ : \ R-\text{ homomorphism}\}$...

So we have the standard diffraction equation for crystals, being: nλ = 2dsinθ. If we keep the wavelength and the lattice parameter the same then n simply depends on θ. So there must be a maximum order diffraction ring that you could obtain as once you get to 90° you're essentially going in the...

Hi everyone, I have lots of (potentially dumb) questions about this "project" I'm working on. It's a voice coil actuator, but with things a bit reversed. Here's how a regular voice-coil actuator is constructed: The rod that is inside the coil is a magnet and the outer cylinder continues the...

Homework Statement We previously solved the heat conduction problem in a ring of radius a, and the solution is c into the sum, perform the sum first (which is just a geometric series), and obtain the general solution, which should only involve one integral in ϑHomework Equations...

Homework Statement Consider a homogeneous thin ring of mass 2.5 x 1022 kg and outer radius 3.9 x 108 m (the figure). (a) What gravitational attraction does it exert on a particle of mass 69 kg located on the ring's central axis a distance 3.7 x 108 m from the ring center? (b) Suppose that...

Homework Statement Several planets (Jupiter, Saturn, Uranus) are encircled by rings, perhaps composed of material that failed to form a satellite. In addition, many galaxies contain ring-like structures. Consider a homogeneous thin ring of mass 2.1 x 1022 kg and outer radius 4.3 x 108 m (the...

Homework Statement refractive index of prism=1.45 λ=450nm 50 bright ring are observed find dHomework Equations 2d=nλ/2 The Attempt at a Solution since 50 bright rings are observed n=24 (-24---------0-------------24) if the distance travel=λ/2 constructive interference will happen since the...

Hello, I'm trying to find an equation which describes B(z) inside of a permanent ring magnet that is axially magnetized. Also, depending on if the equation holds true, if the ring magnet will behave as a magnetic mirror. Below is an equation which describes the axial field of such a magnet...

What happens when you apply power to a toroidal solenoid with a iron ring inside? Does the ring move? Does the speed of movement depend on the amount of power? Sorry if this is too easy, I have no education in physic.

Hey! :o Let $R$ be a finite non-trivial ring. We suppose that for each $r,s\in R$ with $rs=0$ then either $r=0$ or $s=0$. I want to show that $R$ is a division ring. Could you give me a hint how we could show that each element $x\in R\setminus \{0\}$ has an inverse? (Wondering)

Homework Statement [/B] A very thin plastic ring (radius R) has a constant linear charge density, and total charge Q. The ring spins at angular velocity \omega about its center (which is the origin). What is the current I, in terms of given quantities? What is the volume current density J in...

Homework Statement When an aluminum ring is placed on ring launcher so that it surrounds the coil, it flies upward when a AC current is applied to the coil. This does not occur when the intact ring is replaced by a split ring (see below). Explain this in 3 sentences or less. Feel free to use as...

I decided to simulate this scene in Lord of the Rings for a project in school with the purpose of calculating the "real" mass of the One Ring. I've done the experiments according to this principle sketch but I have some troubles with calculating the magnetic force that the copper coil is...

Homework Statement A coil of 450 turns is wound uniformly round a cast steel ring. The ring has a crosssectional area of 750mm2 and a mean circumference of 600mm. A flux of 0.825mWb is produced in the ring. (Given that H = 800At/m at that flux). a. Calculate the reluctance of the ring b...

Let $R$ be a commutative ring and let $\text{M}_2(R)$ denote the ring of $2 \times 2$ matrices with coefficients in $R$. (a) Show that the group of units in $\text{M}_2(R)$ is $\text{GL}_2(R) = \left\{A \in \text{M}_2(R): \text{det}(A) \in R^{\times} \right\}$; (b) show tha $\text{GL}_2(R)...

Homework Statement Let F(ℝ) = {ƒ:ℝ->ℝ} define (f+g)(x) = f(x)+g(x) (f*g)(x) = f(x)*g(x) F(ℝ) is a commutative ring. ƒ_0(x) = 0 and ƒ_1(x) = 1 a) Describe all units and zero divisors b) Find a function f such that ƒ≠ƒ_0, ƒ≠ƒ_1, and ƒ^2 = ƒ Homework Equations A unit is an element r ∈ R, which...

Homework Statement This is more of a question that doesn't require formulas as much as common sense. The question goes,"If you have a ring that is heated up, would the hole in the middle get smaller or larger." Homework Equations N/A The Attempt at a Solution I know that when objects are...

So out of bed you get, shower and make breakfast it is only then that you realize you forgot to set your alarm the previous night,, what do you do, leave your breakfast and go back to bed, eat your breakfast and go back to bed, well you are up now you may as well stay up.

Hi, I'm working with a magnetic levitron project and I've borrowed a professional levitron to see how it works. When I remove the back cap, unexpectedly I saw a square shaped magnet instead of ring magnet. But it acts like almost a ring magnet. I'll explain the difference with images below. At...

Homework Statement Given a charged ring in 2-d, what is the e-field inside the ring? Homework Equations Epoint = kq/r^2 The Attempt at a Solution This isn't a homework question, but more of a problem I keep running into whenever I think about it. I assumed it was 0. I came to this conclusion...

Homework Statement A ring of diameter 7.90 cm is fixed in place and carries a charge of 5.20 μC uniformly spread over its circumference. How much work does it take to move a tiny 3.40 μC charged ball of mass 1.50 g from very far away to the center of the ring? Homework Equations V=(KQ)/r^2...

Homework Statement Let R be a ring and suppose r ∈R such that r^2 = 0. Show that (1+r) has a multiplicative inverse in R. Homework Equations A multiplicative inverse if (1+r)*x = 1 where x is some element in R. The Attempt at a Solution We know we have to use two facts. 1. Multiplicative...

Homework Statement Calculate the magnitude and direction of the electric field due to the ring in the point P on the z-axis. Homework Equations Charge distribution on the ring is given by λ(φ)=λ_0\cdot sin(φ). This should result in the total charge on the ring being zero. Electric field is...

Homework Statement Suppose R is a commutative ring with only a finite number of elements and no zero divisors. Show that R is a field. Homework Equations Unit is an element in R which has a multiplicative inverse. If s∈R with r*s = 1. A zero divisor is an element r∈R such that there exists...

can anyone please explain to me why it's not possible to determine accurately the position of a centre of a Newton's ring pattern? I know that in a Newton's ring only the distance between one side of the ring to the other i.e. the diameter can be accurately determined, not the distance from the...

The circumference of the shaded ring is 2πρ however I am struggling to understand how the area, dA, of the ring is equal to (2πρ)dρ? I mean the circumference varies depending on the value of ρ so surely we can't multiply by dρ to yield the entire area of the shaded ring? If we decided to go by...

Just curious. Not sure if this has been discussed already, and I'm not sure what the phenomenon is called, but here's a description: I have a heavy gold class ring that I got from my alma mater. I put the ring face down on the desk, flat, and it can rest like that because the face of the ring...

I have been trying for hours to understand what is physically causing the interferometric rings to contract when the separation of the mirrors is reduced. From the equation: m\lambda = 2Lcos\theta, where m is the number of fringes, if we consider just one fringe at a fixed wavelength...

Homework Statement Theres an object which makes a pendulum motion.Lets suppose we hang the mass to the ceiling.We released the object with inital angle 0 to the ceiling.(I mean the angle between the object and the ceiling is zero).Whats the moment of the Inertia to the point A. A is a...

I am an eleventh grade student currently in AP Physics C. My teacher did a demonstration with an electromagnet where he drew AC current from the wall to shoot a conductive ring. I was wondering where i could find the blueprint for such a device, or perhaps receive some guidance on how many coils...

I am reading P.M. Cohn's book: Introduction to Ring Theory (Springer Undergraduate Mathematics Series) ... ... I am currently focused on Section 2.3: Artinian Rings: The Semisimple Case I need help with some comments made by Cohn in the introduction to Section 2.3 ... The relevant comments by...

Homework Statement Electric charge Q is uniformly distributed around a thin ring of radius "a".Find the potential at a point p on the axis of the ring at a distance x from the centre of the ring. Homework Equations ##r##=##√x^2+a^2## The Attempt at a Solution \ [/B] I just want to ask...

Homework Statement Two small bar magnets X and Y are released from rest at the same height above the ground. X falls directly to the ground, but Y passes through a metal right which is fixed with its plane horizontal. Does X reach the ground: (A) at the same time as Y, (B) before Y, (C) after...

Homework Statement Consider the ring of polynomails in two variables over a field K: R=K[x,y] a)Show the elements x and y are relatively prime b) Show that it is not possible to write 1=p(x,y)x+q(x,y)y with p,q \in R c) Show R is not a principle ideal domain Homework Equations None The...

Hey! :o When we want to have solutions of a linear differential equation of first order $$ax'(z)+bx(z)=y(z)$$ in a ring $R$, does $y$ have to be an element of the ring? Or is it possible that $y$ is a function that does not belong to $R$ but the solution of the differential equation is in $R$...

How was the equation for area of a ring derived?

Hey! :o What could we change at the following definition so that $\text{EXP}(\mathbb{C})$ is a ring? "We define EXP($\mathbb{C}$) to be the the set of expressions \begin{equation}\label{a} a=\alpha _0+\alpha _1e^{\mu_1z}+\dots +\alpha _Ne^{\mu_Nz} \end{equation} (beyond the `zero...

Homework Statement A ring of mass m slides on a smooth circular hoop with radius r in the vertical plane. The ring is connected to the top of the hoop by a spring with natural length r and spring constant k. By resolving in one direction only show that in static equilibrium the angle the...

Since the time of Darwin, biologists have looked at the history of life as a tree showing how the common ancestor of all life gave rise to all extant species. However, as we have learned more about biology, we've found that organisms do not inherit genetic information from only their direct...

Homework Statement Let A be the algebra \mathbb{Z}_5[x]/I where I is the principle ideal generated by x^2+4 and \mathbb{Z}_5[x] is the ring of polynomials modulo 5. Find all the ideals of A Let G be the group of invertible elements in A. Find the subgroups of the prime decomposition.Homework...

So I am working on the problem of the particle bound to a ring of radius R. I am trying to solve it two ways, as a standing wave and as a running wave. I'm stuck right now solving for the standing wave. So far I have: ψ(x)=Asin(kx) + Bcos(kx) I know that it is periodic from 0 to 2π so if I...