Rings Definition and 437 Threads

Inspired by micromass' statistics challenge, I hope you enjoy it! Recently your financial situation has been less than optimal, and you are left with no other choice but to beg for money in the square in front of the king's palace. However, begging is strictly forbidden in that particular...

How many Einstein rings have been found to date, i mean galaxies lensed by gravity?

I have seen what looks like Newtons rings interference pattern in transverse CT images of 2 solid water block on top of each other. My understanding is that Newtons rings occur in visible light eg photography or scanners. Can anyone shed some light on this? :)

Can somebody explain why this shouldn't surprise me? Apparently it's a corollary of the Akizuki–Hopkins–Levitzki theorem but the proof of that theorem isn't helping me really understand what's going on.

How many NMR signals and peaks will there be for a di-substituted benzene ring and why? The ring has one CH3 and and a Cl ortho to the CH3. (This isn't a homework problem but I am running into same issue whenever I encounter rings wrt NMR) i am specifically confused as to how to apply...

Can you give an example of two rings R and S, and a function f:R⟶S such that f(ab)=f(a)f(b) for all a,b ∈ R, but f(a+b)≠f(a)+f(b) for some a,b ∈ R. I know that it has to do with proving homomorphisms/isomorphisms but am confused how to come up with the actual example.

I seem to be having a difficult time trying to figure out how to do this problem. It's from a non-graded homework assignment. I was able to get every other problem except for this one.Let R = Z, together with the two operations: a + b := a + b + 3 and ab := ab + 3a + 3b + 6 Let S = Z, together...

I was wondering if many members liked the lord of the rings and also it is hard to find people who like to talk about it in person so I thought this could be a place to discuss it anyway.

The other morning it was misting. In the yard the nightlight glowed. Around it the pulsing AC was visible as it appeared to make small rings that moved outward directly, the observers(like an electron as it gets more excited for ex.) We also noticed that the image/rings appeared to be only two...

Most processors have 4 rings. Why do operating systems only use 2. Historical reason ? Overhead ? There is no need for more than two rings ?

Why sometimes rings are observed round the moon or sun? My book says When the moon or sun is observed through a thin layer of high clouds,reflection of light from fine icy crystals,present in the clouds,results in the formation of rings. Can someone please elaborate on that so that I can...

I have a charged ring with a high voltage potential. As I see it the charges repel from each other and so position themselves around the outside of the ring. I want to push the charge to the inside surface of the ring and so I envisioned a 2nd ring positioned concentrically just outside this...

Hi I am currently looking at Newtons Rings, i have changed my refractive index to water (distilled), i have found the rings and they seem to be as aspected except they are extremely faint barely readable infact would anyone know a cause or soulation to this?

why do we can't see Newton's ring through our naked eye?why do we need microscope? but interference pattern due to oil film or soap bubble can be seen through naked eye

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...

In the beginning of his graduate level textbook: Ring Theory, Louis Halle Rowen makes the following statement: "In the solar system of ring theory the Sun is certainly the semisimple Artinian ring ... ... "Can anyone explain why Rowen might say this? Do MHB readers agree? Peter

I am reading P.M. Cohn's book: Introduction to Ring Theory (Springer Undergraduate Mathematics Series) ... ... I am currently focused on Section 2.2: Chain Conditions ... which deals with Artinian and Noetherian rings and modules ... ... I need help with understanding a feature of the Theorem...

If I'm not mistaking , all DC and also universal motors have a brushed commutator not a slip ring commutator because the rotor wires need to keep the same current direction as they rotate pass the same magnetic stator pole. so the only DC motor which could operate on slip rings is a homopolar...

I am reading the book "An Introduction to Rings and Modules with K-theory in View" by A.J. Berrick and M.E. Keating ... ... I am currently focused on Chapter 3; Noetherian Rings and Polynomial Rings. I need help with the proof of Theorem 3.1.4. A brief explanation of the proof precedes the...

I am reading the book "An Introduction to Rings and Modules with K-theory in View" by A.J. Berrick and M.E. Keating ... ... I am currently focused on Chapter 3; Noetherian Rings and Polynomial Rings. I need help with yet another aspect of the proof of Proposition 3.1.2. The statement and...

I am reading the book "An Introduction to Rings and Modules with K-theory in View" by A.J. Berrick and M.E. Keating ... ... I am currently focused on Chapter 3; Noetherian Rings and Polynomial Rings. I need help with another aspect of the proof of Proposition 3.1.2. The statement and proof of...

Say I have the algebra \mathbb{Z}_5[x]/I where is the I is the principle ideal generated by x^2+4. How do I find the ideals in A? I can't seem to find an explanation that is clear anywhere. Thanks!

I am reading the book "An Introduction to Rings and Modules with K-theory in View" by A.J. Berrick and M.E. Keating ... ... I am currently focused on Chapter 3; Noetherian Rings and Polynomial Rings. I need help with the proof of Proposition 3.1.2. The statement and proof of Proposition 3.1.2...

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...

1. The problem statement, all variables and given/known dat Why gold rings are not made from pure gold but mixed with other metals? Homework EquationsThe Attempt at a Solution [/B]my answer...because when two elements are combined chemically they produce a new compound and this avoids...

The Lords of the Rings among centaurs (Phys.org)—Chariklo, the largest known centaur object, orbiting in a region between Saturn and Uranus, is a very intriguing celestial body that surprised astronomers last year. This remote minor planet has unveiled the existence of its rings during a...

why the width of dark ring decreases as we go away from the center in Newton's rings experiment?

I have just finished a post entitled: http://mathhelpboards.com/linear-abstract-algebra-14/irreducible-polynomials-quotient-rings-rotman-proposition-3-116-a-16163.htmlon the Linear and Abstract Algebra Forum ... I want to have the following code recognised: k(z) \subseteq \text{ I am } \phi...

I am reading Joseph J. Rotman's book: A First Course in Abstract Algebra with Applications (Third Edition) ... I am currently focused on Section 3.8 Quotient Rings and Finite Fields ... I need help with an aspect of the proof of Proposition 3.116 Proposition 3.116 and its proof reads as...

I am reading Paul E. Bland's book, "The Basics of Abstract Algebra". I am currently focused on Chapter 6: Polynomial Rings. I need help with an aspect of Theorem 6.3.17. Theorem 6.3.17 requires awareness of the notation of Definition 6.3.15 which reads as follows...

I am reading Joseph J. Rotman's book: A First Course in Abstract Algebra with Applications (Third Edition) ... I am currently focused on Section 3.7 Irreducibility... I need help with an aspect of the proof of Theorem 3.97. Theorem 3.97 and its proof read as follows: Now, the first part of...

Hi, I have to write a program in python (for school) that simulates a specific structure. I choosed saturn's rings. I've started by wrinting an N-body code. My goals are explaining the divisions in saturn rings as cassini division. I don't know if it's a great subject. The teacher told us to...

I was reading a post by spongebob_79 about using counter-rotating rings to generate power and I had a thought. What is the general opinion of using counter-rotating rings mounted to 2 facing sides of a structure and simpily inducing opposite spins on the structures to generate power? Obviously...

I am reading Joseph J. Rotman's book: A First Course in Abstract Algebra with Applications (Third Edition) ... I am currently focused on Section 3.5 From Numbers to Polynomials ... I need help with Example 3.76 ... ... the example concerns Euclidean rings and their defining characteristics so...

I am reading W. Keith Nicholson's book: Introduction to Abstract Algebra (Third Edition) ... I am focused on Section 4.3:Factor Rings of Polynomials over a Field. I need some help with the proof of Lemma 2 on page 223-224. The relevant text from Nicholson's book is as...

I am reading W. Keith Nicholson's book: Introduction to Abstract Algebra (Third Edition) ... I am focused on Section 4.3:Factor Rings of Polynomials over a Field. I need some help with the proof of Part 1 of Lemma 1 on page 223-224. The relevant text from Nicholson's book is as follows...

It's very recent, but it discusses the question of cause of and stability of Saturn's and other ring systems. I came to this site wondering about them. I got the impression from answers received here they were well understood? This paper seems to suggest there are a number of big questions, and...

I am reading Paolo Aluffi's book, Algebra: Chapter 0. I have a question related to Aluffi's description of monoid rings ... ... In Chapter III, Section 1.4 on monoid rings, we read the following: In the above text we find:"Given a monoid (M, \cdot ) and a ring R, we can obtain a new ring...

Homework Statement A uniform rod of mass 3.15×10−2kg and length 0.380m rotates in a horizontal plane about a fixed axis through its center and perpendicular to the rod. Two small rings, each with mass 0.250kg , are mounted so that they can slide along the rod. They are initially held by catches...

http://www.news.com.au/technology/science/aussie-student-proves-existence-of-plasma-tubes-floating-above-earth/story-fnjwlcze-1227379756018

large facilities like CERN have multiple rings of different diameters to prep the beam for the main ring. I get this is something like gears in a truck. my question is what are the broad design constraints for choosing a specific number of rings of a specific diameter?

So this question asked me to determine whether this compound was aromatic, antiaromatic, or nonaromatic and also asked how many pi electrons there were. I figure since there are four groups of electrons the carbanion is sp3 hybridized and I think I'm correct because that is what this thread...

If the image we obtain from Cherenkov light is actually the projection of a continuous wave front (Fig. 1) on a vertical plane, orthogonal respect to the direction of propagation of the incident particle, why we just see a ring (Fig. 2), instead of a full circle? Is it because Cherenkov light is...

Homework Statement Prove the following theorem: Let R be any ring and let f =! 0 and g =! 0 (they don't equal zero) be polynomials in R[x]. If the leading coefficient of either f or g is a unit in R, then: 1) fg =! 0 in R[x] 2) deg(fg) = deg(f) + deg(g) Homework EquationsThe Attempt at a...

If light is transmitted at a point of contact in Newton's rings. The central spot will be darker or brighter?

I am temporarily switching my studies from abstract algebra to mathematical analysis. I am thinking of reading the following book: Principles of Mathematical Analysis by Walter Rudin. What books to MHB members advise me to use in order to gain a full understanding of undergraduate level...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Section 2.2 on free modules and need help with the proof of Proposition 2.2.11. Proposition 2.2.11 and its proof read as follows: Proposition 2.2.11 relies on the definition of an IBN-ring so I am providing...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Section 2.2 on free modules and need help with the proof of Proposition 2.2.10. Proposition 2.2.10 and its proof read as follows:My question/problem is concerned with Bland's proof of Proposition 2.2.10...

I am reading Paul E. Bland's book, "Rings and Their Modules". In Chapter 1: Basic Properties of Rings and Modules, Bland gives endomorphism rings as a basic example of a ring. The example (Example 7) reads as follows:https://www.physicsforums.com/attachments/3572 I do not feel that I fully...

Hi, I have a very simple test bench set up with a HeNe laser, followed by a spatial filter, then an Iris and then a couple of lenses. I can observe many fresnel rings on my image plane. Changing the size of the iris, and its distance changes the number of of rings. I would like to know why...