Rings Definition and 418 Threads

Homework Statement If the apparatus for showing Newton's rings is illuminated with light at 6250 A (angstroms), what thickness of film underlies each of the first three light rings? Homework Equations 2D (the thickness of the film) equals a multiple of 1/2 of a wavelength 1 angstrom =...

Homework Statement In a Newton's Rings experiment, involving a curved lens on a glass surface, what might have happened to the set-up to see a bright spot at the centre? 2. The attempt at a solution Well I know that normally we get a dark spot at the centre because of the lambda/2 phase...

[SOLVED] Algebra question - rings and ideals Homework Statement Let R be a (nonzero) commutative ring with identity and I be an ideal of I. Denote (I) the ideal of R[x] generated by I. The book says that (I) is the set of polynomials with coefficients in I. Why is that? The Attempt at a...

One of my books defines a relation which is "evidently" an equivalence relation. It says that two idempotents in a ring P and Q are said to be equivalent if there exist elements X and Y such that P = XY and Q = YX. The proof that this relation is transitive eludes me. There is so little...

Do all rings have to be generated by ideals? Or can some rings come without ideals? Can some elements in rings be generated by ideals (in ways that other elements of rings are untouched by ideals?) If ALL of a ring's elements are generated by ideals, is there something special about the...

[SOLVED] rings with unity Homework Statement Corollary 27.18 (in Farleigh) tells us that every ring with unity contains a subring isomorphic to either Z or some Z_n. Is it possible that a ring with unity may simultaneously contain two subrings isomorphic to Z_n and Z_n with n not equal to m...

What are these? Is it like some 'physical ring' where you out a wire through it or just a connection to make both input to the op-amp common? How does this really help? Seems like you're making a source common to both like gnd so if the gnd is noisy it becomes common for both and rejects it...

So I'm kind of confused about the definition: a-b\in I Why a - b instead of a + b?

Hi all, I have read this article about Saturn rings: http://www.space.com/news/ap-071213-saturn-ringage.html The author argues as: Quotes: "The notion that Saturn's rings may be a permanent feature was based on observations by the ultraviolet spectrograph instrument on Cassini, which...

can someone please explain what these mappings really means? like what is being mapped and mapped to..?? i get confused by the direct sum & product that gets mapped.. Z \oplus Z ->Z Z -> ZxZ

Homework Statement I want to show that the homomorphism phi:A(X)->k+k given by taking f(x_1,...,x_n)-> (f(P_1),f(P_2)) is surjective. That is, given any (a,b) in k^2 (with addition and multiplication componentwise) I want to find a polynomial that has the property that f(P_1)=a and f(P_2)=b...

Hi all, my question is: -Are there any possibillities that the rings around Satturn will become satellites one day? Thank you.

My professor wrote that we get a Boolean algebra from a Boolean ring (R,+,-,.,0,1) by setting xANDy=xy, xORy=x+y+xy and xNOT=1+x. But it seems to me that xNOT is not an involution. I.e., (xNOT)NOT = 1+(1+x), which is not x. (xNOT=-x would do the trick though)

Anyone know that result? Comments? How is it connected to algebra in general and what kind of algebra is it part of? It is obviously about rings but what else is it part of?

Two rings with radius R and r are let down in the soap water. Between them pellicle appeared (like in image). Image: here all are symmetric ;) problem: need to find y=f(x) what i think:volume of figure is minim. maybe express volume via needed function, then get minimum of volume, and find...

This is the last question in Elements of Abstract Algebra by Allan Clark. When is (q) a prime ideal in Z(\rho) (the Kummer ring) where \rho = e^{2\pi i /p}, where p and q are rational primes. This seems to be a difficult question to answer in general... since considerable effort goes into...

I have a trouble proving that a finate (nonzero) commutative ring with no zero divisors must have an identity with respect to multiplication. Could anybody please give me some hints? I do know all the definitions (of ring, commutative ring, zero divisors, identity) but have no idea how to go...

Suppose A is a Noetherian ring, phi:A->A any surjective ring homomorphism. Show that phi is also injective. Also, if all the prime ideals of a ring A are finitely generated then is A noetherian? I'm pretty sure it is. I figure I can take all of the ideals that are not finitely generated...

In the statement of Maschke's theroem we are told 'Let G be a finite group and F a field in which |G| not equal to zero. As an example we are told if our group was C2 (cyclic) then we could not have F=F2 (the field with 2 elements). I fail to see how C2 and F2 are related, surely |C2|=2...

I am having a very hard time with a general concept of proving something. If I have some arbitrary function mapping one ring, let's say R, to another ring, S, and want to prove that R is isomorphic to S, then I need to show that there exists a bijective homomorphism between R and S. But how do I...

[b]1. I am just looking for a defn, I can't find it on the net: Given a ring R, a, b elements of R, (a?) gcd(a,b) is defined to be? [b]3. I am guessing that if d/a and d/b and for any other e such that e/a and e/b we have e/d, then d is (a?) gcd of a and b. Is this correct, and is...

Homework Statement A plano-convez lens (flat on one side, convez on the other) rests with its curved side on a flat glass surface. The lens is illuminated from above by light of wavelength 521 nm. A dark spot is observed at the centre, surrounded by 15 concentric dark rings (with bright rings...

Question: Let R be a ring of characteristic m > 0, and let n be any integer. Show that if 1 < gcd(n,m) < m, then n · 1R is a zero divisor heres what i got out of this: Let gcd(n,m) = b 1< d < m so m/d = b < m and d | n Also, m * 1_R = 0 can someone please offer some...

Let R be a ring of characteristic m > 0, and let n be any integer. Show that: if 1 < gcd(n,m) < m, then n · 1R is a zero divisor heres what i got out of this: Let gcd(n,m) = b 1< d < m so m/d = b < m and d | n Also, m * 1_R = 0 can someone please offer some insight...

Figure 35-46a shows a lens with radius of curvature R lying on a flat glass plate and illuminated from above by light with wavelength . Figure 35-46b, a photograph taken from above the lens, shows that circular interference fringes (called "Newton's rings") appear, associated with the variable...

How does a Goebner basis relate to Ideals and how does it help solve otherwise extremely complex systems of equations? Part of what I'm working on involves trying to solve V=0=\partial_{i} V for V a quotient of polynomials in several variables. This paper talks about using the Groebner basis...

Using the theorem that in any boolean ring a+a=0 for all a in boolean ring R. Then 0 is in R. Make the multiplicative identity 1 is also in it. Therefore R can only take 0 and 1 and no more because 1+1=0. 0+0=0. 1+0=1 always. So 2 or other elements can never occur.

Quotient ring is also know as factor ring but what has it got to do with 'division' in any remote sense whatsoever? I know it is not meant to be division per se but why give the name of this ring the quotient ring or factor ring? What is the motivation behind it? R/I={r in R| r+I} Normally...

Homework Statement I am required to prove that F_5[x]/(x^2 + 2) isomorphic to F_5[x]/(x^2 + 3) now I have the solution in front of me so I more or less know what's going on, however there are some points of confusion... ...the solution states that x \rightarrow 2x will define the...

I am required to show that F5[x]/(xsqd + 2) and F5[x]/(xsqd +3) are isomorphic, any hints on how to go about this question?

Does cosets exist in rings? i.e R = Ring, a in R set {a*R} or set {a+R} The above two sets looks very similar to cosets in groups but there are two operations in rings so potentially two different cosets both involving the same ring R and element a. If the above two sets are not...

I know this isn't really 'earth sciences' but there is no planetary forum that I am aware of. Anyway, why does Saturn have rings, and what are they made of? I read somewhere that Enceladus is the major souce of Saturn's largest ring, the 'E-ring'. What does that mean...

I've already completed 1), but it's necessary for one to know it for question 2). I'm pretty sure that I've found my homomorphism in 2, but I don't know whether or not is unique. How do I show a homomorphism is unique in this case? Problem 1: Let R be a commutative unital ring, and let S be a...

Is there a simple method for finding all the units in a polynomial quotient ring over a finite field? For example: {F_2[x] \over x^7-1} I can see the easy ones like 1, and all power of x, but I wanted a general rule or method for finding all of them if it exists (besides testing each...

Figuring sum of double bonds and rings ?? Does anyone know how if there is a way to figure out the sum of double bonds and rings of a compound C6H9BrO ?? Lost.. thank you.

I won't say who said it, but does this sound right to you? Dendrochronolgists on TV all say it so easy, you count the tree rings and the space in between, and that will tell you about the temperature and precipitation and how long the tree lived. Also: This sounds kind of dumb, but what about...

Hi. I have some homework questions here that I need a little help on. I know the fomulae to use just do not know how to apply it properly. Any help will be appreciated. In a Newton's Ring experiment, a planoconvex glass (n=1.54) lens having a diameter 14.3 cm is placed on a flat plate. When...

http://hubblesite.org/newscenter/newsdesk/archive/releases/2005/33/full/

Let p,q be two prime numbers. Prove that there exists a homeomorphism of rings such that f([1]_p)=[1]_q from Z_p[X] into Z_q[X] if and only if p=q. I believe that the converse of the statement is trivial but the implication seems to be obvious? I really don't know what there really is to...

Hello, I would be interrested in comments, references, books, papers and web pages regarding the problem of mechanical contact between two rings. The attached picture describes the geometry of the problem: a ring (tube) is resting on the bottom of a larger ring (tube). These two rings are...

http://hosted.ap.org/dynamic/stories/S/SATURN_RINGS?SITE=TNNAT&SECTION=HOME&TEMPLATE=DEFAULT

Some of the squabbles over how the immense profits from the "Lord of the Rings" are to be divided, have now been settled out of court, according to this article: http://news.independent.co.uk/world/americas/article309203.ece Still, a lot of quarrels remain; in particular, Peter Jackson&Fran...

Hi all, I'd like to know what these rings at high voltage connectors are good for: http://www.surplec.com/hvt_polemount_shipping.jpg http://www.surplec.com/hvt_inventaire_15.jpg http://www.recursivemediaone.com/high%20voltage%203%20gs.jpg

A steel sphere sits on top of an aluminum ring. The steel sphere (a (average coefficient of linear expansion) = 1.1*10^-5/C) has a diameter of 4 cm at 0 C. The aluminum ring (a = 2.4*10^-5/C) has an inside diameter of 3.9940 cm at 0 C. Closest to which temperature given will the sphere...

The Other Day I Was Sitin In A Bar Looking At My Freinds Smoking , They Tried And Tried To Blow A Smoke Ring But Could'nt ,it Ws Agreed That Its Not Possible To Create Smoke Rings At Will ,its A Flash In The Pan , But I Differed ,surely Their Must Be Some Condition For Creating A Smoke Ring ,i...

I'm just starting rings and I don't think I really understand them. When an operation is shown as a grid where the entry i, j in the grid is the element (i op b), I can see immediately what the commutative property looks like (grid symmetric about diagonal from top left) and what a unit, a...

Most giant planets we know of are Gas Giants. Is it possible for a planet made of rocks to be the size of jupiter? In other words is it possible for a Rock Giant? Also, is it also possible for a rocky planet to have rings around it like Saturn? Though we have found no rocky planet with rings...

Those of you stressing over grad school should read this ... funny stuff. (I am not the author, by the way, I just found it amusing). http://www.livejournal.com/users/capthek/224706.html

...then you'll probably like playing this: Kings of Chaos

I don't really know where this thread belongs. I trust the mentor to move it, if necessary. How do mood rings work? How accurate are they? As always, any and all relevant information is appreciated.