Ring Definition and 1000 Threads

How does one compute the number of ring homomorphisms from \mathbb{Z}_2^n to \mathbb{Z}_2^m? Or, likewise, the number of linear mappings on those two vector spaces?

Does bromobenzene mean that a bromine is bonded to every carbon in the benzene ring? When it saids 1-ethylbenzene where do i put the ethyl since benzene is in a ring? Thx in advance

Happy New Year! Yay! Its going to be the new year in about 5 hours and 10 minutes for me. Happy NEW YEAR fellow PFers!

Why can't stuff like this ever happen to me? :frown: "An anonymous gift-giver left a $15,000 diamond engagement ring to the owner of an unlocked car in western Massachusetts with a typed note hinting at a broken heart. "Merry Christmas. Thank you for leaving your car door unlocked...

i uploaded my calculations, please check them out and point out the errors, it doesn't make any sense to me. i changed the file, now its readable (and if it needs more clearification please say so and i will rewrite it again. (see attachment)

Its from an example in the book, and it doesn't seem to make sense, A rod of length l has a uniform positive charge per unit length (lambda) and a total charge Q. Calculate the electric field at a point P that is located along the long axis of the rod and a distance a from one end. So...

I have this question, just curious if what I did is correct. ---- Let A and R be rings, and let f:A->R be a function satisfying: f(a+b) = f(a)+f(b) and f(ab) = f(a)f(b). Prove that if f is surjective, then f(1) = 1. ----- Note: I will use * for multiplication for clarity where things would...

what is the easiest way to show that Q[x]/<x^2-2> is ring isomorphic to Q[sqrt2]={a+b(sqrt2)|a,b in Q} just give me a hint how to start

Let R be a commutative ring and let I be an ideal in R. 1. If every ideal in R is principal, then every ideal in R/I is principal. 2. If every ideal in R/I is principal, then every ideal in R is principal. I must prove or disprove if either is true or false. Can someone tell me whether either...

"Let F be a field and let f:F->R be a ring homomorphism satisfying f(0) != f(1). Show that f is necessarily injective." Assume f(a)=f(b), then f(a)-f(b)=0R => f(a-b)=0R. f(0F)=0R and therefore a=b. But this implies that every homomorphism is injective. How can that be?

i know that if you want to figure out how many electrons an atom has on its outer ring (valence?), its 1 for group 1 (eg Na), 2 for group 2 (eg Mg), all the way to 7 for halogens and 8 for noble gases. however, how do you figure it out for transition metals in the middle? for example...

How would I prove that x^2+1 is irreducible in Z_p[x], where p is an odd prime of the form 3+4m. I know that for it to be rreducible, it has to have roots in the ring. So x^2=-1 (mod p). Or x^2+1=k(3+4m) , for some k. I tried induction on m, but it does not work because [itex}x^2+1[/itex]...

It is a controversial issue of whether or not Thomas Nast's cartoons lead to the collapse of the Tweed ring. Some view him as a rasist and that the Times and Samuel Tilden did more, but others feel that he was able to effectively shift the opinion of the general population. I would like to see...

The ring is a two dimensional figure. Given that the line charge density "U", what can we say about the Eletric field everywhere inside such a ring of charge?

Jillian angrily throws her engagement ring straight up from the roof of a building, a height 11.5 above the ground, with an initial speed of 4.95 . You may ignore air resistance. For the motion from her hand to the ground, what is the magnitude of the average velocity of the ring? Isn't...

can anyone give me examples of: 1.finite non-commutative ring with identity 2.finite non-commutative ring without identity

Prove if a ring has a unity, then it is unique: Here is what I have so far: Proof: Assume there exists a ring R that contains two distinct unity's, call a and b, where a != b. By the definition of a unity, we get ax = xa = x and bx = xb = x for all x != 0 in R. So, ax = xa = bx = xb = x. If...

I'm looking for a text that goes into detail on the workings of laser ring gyroscopes. If it also included information on fiber optic gyroscopes that would be a bonus. I have looked a bit, however either my "googleing skills" aren't up to par or it's way too specific/fringe a subject. Any...

I want to show that if I and J are coprime ideals of a ring R, so I+J=R, then for any positive numbers m and n we also have I^n+I^m=R. I thought the easiest way to do it was to show that 1 \in I^n+J^m given that there exist i\in I and j\in J such that i+j=1. But I haven't had much luck yet...

I'm working on a problem about the endomorphism ring: Let R be a ring. Show that R is isomorphic to E = { f in End(R+) | f(xr) = f(x)r for all x,r in R } I'm trying to do it with the following theorem in our lecture notes: Let R be a ring and R+ the additive group of R. Let for r in R, L_r...

This is a stupid question but how? I have a "halve ring" slightly above the other "halve ring". This happens all the time with my binders. Somehow one of my binders got fixed? So it should be possible to fix manually.

In a uniformly charged ring of radius r, if there is an imaginary line from the center of the ring extending outward || || || ||-----------------X-------------------------------> infinity || || || At the center of the ring I am told the charges cancel so the net charge is zero. And at...

I've designed a electromagnetic vibration shaker but I've problems at high frequencies(200 Hz and upper) and I've heard that I can compensate it by a Copper ring,please comment me...Bahram

whats a ring ?

I thought people helped on this forum? If anything is unclear just ask, I'm checking for posts every minute. Come on people I have to get this done by 5 pm. I've gotten a little further. I believe it has something to do with mutual inductance. A metal ring (no current) is brought close to a...

when considering the brown ring test to test NO3- do you first have to mix NO3- and H2SO4 together and then put newly made FeSO4 or first mix NO3- and newly made FeSO4 together and then pour H2SO4 or does it it make any difference either way

A brass plug is to be placed in a ring made of iron. At room temperature (20oC), the diameter of the plug is 8.755 cm and that of the inside of the ring is 8.745 cm. They must be brought to what common temperature (in Co) in order to fit? The coefficient of linear expansion for brass is...

End n(k) is the set of all polynomial mappings: k^n->k^n. i have to prove that end n(k) is a monoid. k is a field of q elements and n is the number of variables. the composition of two mappings F G is: F o G = F o G(v) = [F1(G1(v),..Gn(v)), ... Fn(G1(v),...Gn(v))] i must prove that the...

I spent like 6 hours trying to prove that the endomorphism ring of a simple module is a field, helping my friend with his homework. Now I'm convinced that the result is not true. By Schur's lemma, all endomorphisms of a simple module (except 0) are isomorphisms, so it's a division ring, but I...

Hello, I'm a bit stumped on a problem and wondered if anyone knew how to approach this problem: When a Newton's ring apparatus, ( Fig. 24-30(see attached) ) is immersed in a liquid, the diameter of the eighth dark ring decreases from 2.99 cm to 2.49 cm. What is the refractive index of the...

A proposed space station includes living quarters in a circular ring 50.3 m in diameter. At what angular speed should the ring rotate so the occupants feel 0.411 g where g is the gravitational acceleration on the surface of the Earth?

determine all the ideals of the ring Z[x]/(2,x^3+1) i'm a bit confused b/c this is a quotient ring. would the ideals be all the polynomials which are multiples of x^3+1, with their free term an even number ?

Can someone please explain to me how to calculate chemical shifts only given a few constants? For example the compound is as follows: a benzene ring except in positions 1 and 4 there is an OCH3 group. given only the values of: alkane CH3 = 0.9 alkane CH2 = 1.3 alkane CH = 1.4 O=C-CH3...

im working on a lenz's law experiment where i am making an aluminum ring levitate on an iron pole, but I am not sure of the theory behind how it works, and what i should be writing about. any suggestions welcome.

little bit stuck on a problem, here goes: A ring of mass 2.4 kg with an inner radius 6cm abd outer radius 8 cm is rolling (without slipping) up an inclined plain that makes an angle of 36.9* with the horizontal. At the moment, the ring is 2m up the plane its speed is 2.8 m/s. The ring...

Primes in ring of Gauss integers - help! I'm having a very difficult time solving this question, please help! So I'm dealing with the ring R=\field{Z}[\zeta] where \zeta=\frac{1}{2}(-1+\sqrt{-3}) is a cube root of 1. Then the question is: Show the polynomial x^2+x+1 has a root in F_p if...

Is the beauty and color to the Ring Nebula due to synchrotron radiation of particles (electrons) with higher energy (spin) being blueshifted the closer they are to the white dwarf at the center? If so is it the magnetic field that spins the electrons intensly and the futher away the electrons...

Hello all, first time to the site and its very helpful! I wish I would have found it sooner. I am stuck on quotient rings. Here is my question.. How do I find elements of a quotient ring? It asks me to list all elements of a quotient ring. Anybody have any ideas how i can find them...

Let f: Z \rightarrow F be a ring homomorphism from Z onto a field F. Prove that F must be finite with a prime number of elements. How would one go about proving this? I understand that multiplication and addition must be preserved in a homomorphism. I guess I must somehow show that a proper...

Why does the point singularity of a black hole turn into a ring if the BH is spinning? What would the singularity look like if the BH were spinning on 2 axes? (What if the BH were really a multi-dimensional construct and were spinning on more axes?) What is the volume of a ring singularity...

I'm having trouble with this problem... A ring (mass = M) is suspended by an ideal cord from the ceiling, two equal masses (mass = m) are released from the top of the ring and slide down, one on either side of the ring, without friction. The question is: What condition must the masses meet...

Today's Astronomy Picture of the Day is a photograph showing a rainbow ring, inside of which is a bright region. APOD also carries a challenge - what is the explanation for sequence of colours and the bright region? Surprisingly, lots of bright students, knowledgeable teachers - even the...

Does anybody know who first introduced terms ring and field and when?

Ring, field, injection, surjection, bijection, jet, bundle. Does anybody know who first introduced those terms and when and why those people called these matimatical structures so. I mean not the definitions but the properties of real things which can be accosiated with those mathematical...

I think the title describes my question fairly well. Could someone please explain to me the difference between a field and a ring? While you're at it, feel free to explain the concept of "mod." I see these all the time when I'm reading, but I've never had anyone to tell me what they actually...

I'm having a very tough time understanding homomorphisms and ideals, probably because I'm very fuzzy with the concept of rings. I'm stuck on the following problem: Find all the ideals in the following rings: 1. Z 2. Z[7] (Z subscript 7, equivalence classes of 7 I'm guessing) 3. Z[6] 4...

An annular ring of aluminum is cut from an aluminum like attached. When the ring is heated, 1)the hole decreases in diameter 2)the area of the hole expands the same percent as any area of the aluminum 3)the area of the hole expands a greater percent than any area of the aluminum...

Another question, in which I believe I've gotten the same wrong answer two different ways now. Muons have a mass m = 105 MeV/c^2. They are accelerated to a kinetic energy of 2 TeV in a storage ring with radius r = 2 km. A student speculates that since muons have a lifetime of only T =...

How can I show that if \frac{a}{a^2-2b^2},\frac{b}{a^2-2b^2}\in \mathbb{Z} then a^2-2b^2=\pm 1? If you care to see the whole problem, you can find it here: http://www.math.rochester.edu/courses/236H/home/hw12.pdf It's #4 part c. BTW, why is the significance of this "norm map"? I...

A brass ring of diameter 10.00 cm at 19.5C is heated and slipped over an aluminum rod of diamter 10.01 cm at 19.5C. Assume the average coefficients of linear expansion are constant. a) To what temperature must this combination be cooled to separate them? is this possible? b) If the aluminum...