Rings Definition and 445 Threads

So I just had a question on a quiz (did not go well) about carbocation stability on the fused rings bicyclo[2.2.1]heptane, with the positive charge on a bridgehead carbon and 2-methylbicyclo[2.2.1]heptane with the positive charge on C2. The question was which is more stable and why? The...

Homework Statement This is not an assignment question, just something that I am wondering about as an offshoot of an assignment question. In my course notes Rings are defined as having 3 axioms and commutative rings have 4.(outined below) I have just answered this question: Show that the...

So I've had this nice ring for a while, its the 'This too shall pass' kind of ring given to king Solomon by one of his wisemen. I also have a titanium band ring for my pinky, and a sterling silver blue sapphire skull ring. What fingers do you prefer? I have it on my left pinky, left middle...

There is a small outline in a book about finding the determinant of a matrix over an arbitrary commutative ring. There are a few things I don't understand; here it is: 'Let R be a commutative ring with a subring K which is a field. We consider the matrix X = (x_{ij}) whose entries are...

Homework Statement is the set of all polynomials a ring,and a fieldd.Is is commutative and does it have unity Homework Equations The Attempt at a Solution now if we add or multiply any polynomials we get a polynomial. So it is a ring, but i am not sure what the multiplicative...

Is there anyway that a Ketone on a benzene ring could be reduced to a hydrocarbon with the use of H2, Pd/C, 45 psi ? I know that carbonyls on aromatic rings are able to be reduced to alcohols via this method but would be interested in if it is possible (more so then practical) to fully reduce to...

I need to learn some abstract algebra, and it's pretty hard doing this on my own. Please help me. According to the definition, Ring is an algebraic structure with two binary operations , commonly called addition (+) and multiplication ( . ). We write (R,+, .). Some examples of rings are: (Z, +...

They all seem to be defined as sets with multiplication and addition axioms satisfied. What is the difference?

The first question is to find the ideals of R[x]/<x^2 - x>. I can see that the elements of the factor ring are of the form p(x) + <x^2 - x>, where p(x) is in R[x], which can be simplified to q(x)(x^2 - x) + r(x) + <x^2 - x> = r(x) + <x^2 - x>, where r(x) is of degree 1 or 0. Now I'm pretty much...

After a bit of searching of scholarly text and investigations I have found myself unable to find the next piece of information. Can there exist a vortex ring which travels at supersonic speeds? Not as in the airflow within the vortex ring, there was a paper I was able to acquire about that...

Homework Statement A smooth ring with a mass m is threaded through a light inextensible string .The ends of the string are tied to two fixed points A and B on a horizontal ceiling so that the ring is suspended and can slide freely on the string.A hotizontal force acts on the ring in a...

So we know Newton's rings. I have two concrete questions: 1) Why is the center point black? I quote from my book: "Because there is no path difference and the total phase change is due only to the 180° phase change upon reflection, the contact point is dark." I'm not quite sure what they...

Homework Statement I have to show that \sum ai xi -> (a0 \sum ai) is a ring homomorphism from C[x] to C x C I then have to use the first isomorphism theorem to show that there is an isomorphism from C[x]/ (x(x-1)) to C x C where (x(x-1)) is the principal ideal (p) generated by the element...

Sorry if this is the wrong section (already posted it in the biology forum and got no response) but this question comes from a convo I had with some friends the other night.. Say you were able to grow a full size tree indoors (assuming you had the space, nessesary lighting, soil, etc..) and...

I'm trying to understand Newton's rings. So we have a plano-convex lens supported in a plane (please, see image here http://scienceworld.wolfram.com/physics/NewtonsRings.html). The incident light is divided into the light that is reflected at the convex surface and the light that is reflected at...

Sorry if this is the wrong section but this question comes from a convo I had with some friends the other night.. Say you were able to grow a full size tree indoors (assuming you had the space, nessesary lighting, soil, etc..) and kept it under 18 hours of light and 6 hours of dark...

This may be a dumb question, but I just want to make sure I understand this correctly. For R_{1}, R_{2}, ..., R_{n} R_{1} \oplus R_{2} \oplus, ..., R_{n}=(a_{1},a_{2},...,a_{n})|a_{i} \in R_{i} does this mean that a ring which is a direct sum of other rings is composed of specific elements...

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...

Homework Statement Decide which of the following are subrings of the ring of all functions from the closed interval [0,1] to R (the reals) a) The set of all functions f(x) such that f(q) = 0 for all q in Q (the rationals) & q in [0, 1] b) The set of all polynomial functions c) The set...

why are Newton rings observed in a circuler pattern?

Homework Statement Hi guys, I'm trying to show that \mathbb{F}_5[x]/(x^2+2) and \mathbb{F}_5[x]/(x^2+3) are isomorphic as rings. The Attempt at a Solution As I understand it, I have to find the homomorphism \phi:R\to S which is linear and that \phi(1)=1. I'm just struggling to find...

Hi guys, I'm trying to show that \mathbb{F}_5[x]/(x^2+2) and \mathbb{F}_5[x]/(x^2+3) are isomorphic as rings. As I understand it, I have to find the homomorphism \phi:R\to S which is linear and that \phi(1)=1. I'm just struggling to find what I need to send x to in order to get this work.

Can anyone recommend a book that covers linear algebra through the perspective of modules? I am basically trying to find something that would highlight all the differences between modules and vector spaces. Lam has written the book Lectures on Rings and Modules, which is good, but doesn't...

1. Two 10-cm-diameter charged rings face each other, 19.0 cm apart. Both rings are charged to + 50.0 nC. What is the electric field strength at the center of the left ring? 2. E = q/(4*pi*epsilon*r2 3. Ok, the E field from the left ring is zero at this point due to...

Hello could someone help me out with this question Show that R[x]/(x^2)+a isomorphic to the complex numbers if a>0 and RxR if a<0. Here is an attempt! for mulitplication in R[x]/(x^2)+a Elements of \mathbb{R}[X]/(X^2+a) are cosets: f(X) + (X^2+a). By the polynomial division...

Homework Statement Let R and S be rings. Show that \pi:RxS->R given by \pi(r,s)=r is a surjective homomorphism whose kernel is isomorphic to S. Homework Equations The Attempt at a Solution To show that \pi is a homomorphism map, I need to show that it's closed under addition and...

1. Two 10-cm-diameter charged rings face each other, 19.0 cm apart. Both rings are charged to + 50.0 nC. What is the electric field strength: At the midpoint between the two rings? At the center of the left ring? 2. E = q/4pi*ep_o*r^2 3. The online problem says this is from a...

Homework Statement The problem is to show that a subset A of a ring S is an ideal where A has certain properties. S is a ring described as a cartisian product of two other rings (i.e., S=(RxZ,+,*)). I have already proved that A is a subring of S and proved one direction of the definition of an...

I am interested in semisimple rings and semisimple modules which are not unital. There are two concepts of ring semisimplicity: left semisimplicity and right semisimplicity. A ring is called semisimple on the left if it is presented as a sum of its simple left ideals. A ring is called semisimple...

Ok so I am not a math major and i haven't taken an abstract algebra class but i am curoius about the subject. I have been watching video lectures at UCCS at http://cmes.uccs.edu/Fall2007/Math414/archive.php?type=valid and the proffessor talks about groups and rings. In the introduction the...

What's the difference (if any) between a direct sum and a direct product of rings? For example, in Ireland and Rosen's number theory text, they mention that, in the context of rings, the Chinese Remainder Theorem implies that \mathbb{Z}/(m_1 \cdots...

OK, in bearings (particularly roller) often times there will be a "spring ring" around it. The ring acts to soften the support structure for the bearing. Ring is typically a thin ring with "pads" on both the inside and outside. They are staggered such to put the thin ring into bending when load...

http://news.yahoo.com/s/livescience/20091216/sc_livescience/strangephysicaltheoryprovedafternearly40years" . "Efimov theorized an analog to the rings using particles: Three particles (such as atoms or protons or even quarks) could be bound together in a stable state, even though any two of...

Homework Statement A piece of curved glass has a radius of r=10m and is used to form Newton's Rings. Not counting the dark spot in the center of the pattern, there are one hundred dark fringes the last one on the outer edge of the curved piece of glass. The light being used has a wavelength...

Homework Statement : Hey guys, I'm a new user so my semantics might be difficult to read... Let A={a+b(square root(2)) ; a,b in Q} (i)Describe A as a factor ring of Q[x] ( The polynomial Ring) (ii) Show A is a field The Attempt at a Solution (i) Let x be in C (the...

I was looking at this link: http://en.wikipedia.org/wiki/File:Universe_Reference_Map_%28Location%29_001.jpeg" and wondered to myself why the asteroid belt just outside of Mars is a ring...as opposed to a sphere. Then I thought, why do all the planets seem to orbit the sun on a similar plane...

Homework Statement The following are equivalent for S\subseteqR, S\neq\oslash, and R is a commutative ring with unity(multiplicative identity): 1. <S> is the ideal generated by S. 2. <S> = \bigcap(I Ideal in R, S\subseteqI) = J 3. <S> = {\sumrisi: is any integer from 1 to n, ri\inR \foralli...

Homework Statement The figure below shows two concentric rings, of radii R and R ' = 3.00R, that lie on the same plane. Point P lies on the central z axis, at distance D = 2.00R from the center of the rings. The smaller ring has uniformly distributed charge +Q. What must be the uniformly...

I am having a problem with some abstract algebra and I was wondering if anyone could help and give me some insight. The problem is as follows: Give an explanation for your answer, long proof not needed: Determine U(Z[x]) Determine U(R[x]) These are in regards to rings. I know...

I'm working on a research project involving calculations about various aspects of electron storage rings and have come across the term energy acceptance or energy aperture. Could someone explain to me what is meant by this term? It is used in a lot of literature but I haven't been able to find a...

Effect of a pair of slip rings in a DC motor Hi, I have a question here. Knowingly that the effect of a slip ring in a DC motor is to reverse the direction of the current in a loop whenever the commutator changes contact from 1 brush to another, so as to ensure the loop to be always...

Whilst following my textbooks advice and "proving to myself that the inertia listed are true" I considered the Moment of Inertia of a hollow sphere by adding up infinitesimally thin rings: dI = y^2 dm = y^2 \sigma dS = y^2 \sigma 2\pi y dz = 2\pi y^3 \sigma dz This didn't work...

Homework Statement in order to factorize 20 on the rings of Q( \sqrt 2) i must solve Homework Equations x^{2} -2y^{2}=10 The Attempt at a Solution i do not know how to solve it, i have tried by brute force with calculator but can not get any response , the given hint is that...

Homework Statement Show that a finite commutative ring with no zero divisors is an integral domain (i.e. contains a unity element) Homework Equations If a,b are elements in a ring R, then ab=0 if and only if either a and b are 0. The Attempt at a Solution I've been trying to use...

Homework Statement Let G be a finite group and let p >= 3 be a prime such that p | |G|. Prove that the group ring ZpG is not a domain. Hint: Think about the value of (g − 1)p in ZpG where g in G and where 1 = e in G is the identity element of G. The Attempt at a Solution G is a...

Hi , How to calculate the diploe vector of benzene ring?. what is the formula for calculating the diploe moment?. Thanks in advance Aneesh

Homework Statement Suppose R is a ring and I,J is an ideal to R. Show (i) I+J is ideal to R. (ii) I union J is ideal to R.Homework Equations none

Could anyone direct me to a formula for the area enclosed by two overlapping rings? Sketch below... Thanks... -jg

Why are Saturns rings broken up into many rings? Why don't they all just orbit together in one massive ring.

Hi so this isn't homework its in my book , i just don't get it they skipped this step Let R=Z(i) be the ring of gaussian integers and let A=(2+i)R denote the ideal of all multiples of 2+i Describe the cosets of R/A im just having trouble understaning this step: "Since 2+i is in A we...