Recent content by rayman123

I got it after all :)

Homework Statement Let A be an integral domain with field of fractions K, and suppose that f\in A is non zero and not a unit. Prove that A[\frac{1}{f}] is not a finite A-module. [Hint: if it has a finite set of generators then prove that 1,f^{-1},f^{-2},...,f^{-k} is a set of generators for...

Homework Statement Solve 57x+4y=2 Homework Equations I use the equation 57x+4y=1 find gcd(57,4) as follows 57=14\cdot 4+1 then gcd(57,4)=1 and 1=57-4\cdot 14 so the particular solution to my first equation is x_{0}=2*and y_{0}=-28 Wolfram says it is correct but I am not sure if the...

I am not sure if this is the way we are supposed to do it...Euclid's algorithm is to help to make the calculations easier, without calculator no one can do such divisions... \frac{942578}{1978935}=\frac{314526}{659645} but how can we be sure that this is not further reducible?

Homework Statement reduce the fraction \frac{943578}{1978935} to its lowest terms using Euclid's algorithm The Attempt at a Solution I start with finding the gcd of these two numbers using E.algorithm 1978935=943578*2+91779 942578=91779*10+25788 91779=25788*3+14415 25788=14415*1+11373...

Homework Statement let \varphi:\mathbb{Z}[i]\rightarrow \mathbb{Z}_{2} be the map for which \varphi(a+bi)=[a+b]_{2} a)verify that \varphi is a ring homomorphism and determine its kernel b) find a Gaussian integer z=a+bi s.t ker\varphi=(a+bi) c)show that ker\varphi is maximal ideal in...

thank you :) now I see

the difference is s_{n}-S_{n}=-16

it should be 16, it was a typo but this still does not show me the error

Homework Statement let f(x)=x^2 Calculate upper sum and lower sum on the interval [-2,2] when n=2The Attempt at a Solution since n=2 I divide the interval into [-2,0]\cup[0,2] then on the interval [-2,0] the function f(x)=x^2 has the highest valute at x=-2, f(-2)=4=M_{0} and the lowest value...

didn't you forget <|4|>={[0],[4],[2]} and <|5|>=<[1]>??

I guess 1 is being moved to 4 4 goes to 3 and 3 goes to 1 I do not know...:( I know how to find an inversion for something like that for example \left( {\begin{array}{cc} 123 \\ 231 \\ \end{array} } \right)^{-1}=\left( {\begin{array}{cc} 231 \\ 123 \\ \end{array} }...

Homework Statement Find an inversion of the following cycle (143) Homework Equations (143)^{-1} The Attempt at a Solution Could someone show me how do we compute this?

yeah, you are right :) thank you

My task is to 1) compute the Fourier transform of the function \frac{x}{1+x^2} 2) compute the integral \int_{-\infty}^{\infty}\frac{x^2}{(1+x^2)^2}dx 1) I can write my function as x \cdot \frac{1}{1+x^2} and by using the formula we let f(x)=\frac{1}{1+x^2}...