Recent content by AkilMAI

f:R->S is a homomorphism of rings,such that kernel of f has 4 elements and the image of f has 16.How many elements has R? 16=|Im ( f )|=|R/ker f|=|R|/|ker f|=|R|/4=>|R|=4*16=64 [FONT=MathJax_Math]

Re: Kernerl and homomorphism Thank you for the confirmation

Re: Kernerl and homomorphism ok either ker f=12Z or ker f= {0} f(n)=0>n*f(1)=0 but f(1)=1since f is a ring homomorphism.So ker f={0} or Z/ker f is an integral domain since it is a subring of C =>ker f/=12Z. or ker f=/13 I'm I doing this wrong?

Let f : Z ->C be a homomorphism of rings. Can the kernel of f be equal to 12Z or 13Z? Ok,the way I'm thinking about it is using a proof by contradiction:asuming ker f=12Z...then by the First Isomorphism Theorem for rings Z/ker f ~im f where I am f is by definition a subring of C.But since I am...

if (x+1_r)^2=1_r =>x=-1/2...but x^2=1 so this is a contradiction...therefore x=-1=>|R|=2(because of the powers of x).Correct?

How can I prove that every finite domain has an identity element? How should I think about the problem and what should I take into consideration?

1_R=identity in the ring R. /=...not equal Having some issues with this any help will be great: Let R be a ring with identity, such that x_2 = 1_R for all 0_R /= x ,where x belongs to R. How many elements are in R? Thanks

max(x^2,y^2) with sides of 1?

ok ...how should I proceed?

how will that help?

How can I evaluate I_c |z^2|,where I is the integral and c is the square with vertices at (0, 0), (1, 0), (1, 1), (0, 1) traversed anti-clockwise...?

Complex mapping z → f(z) =(1 + z)/(1 − z) 1.What are the images of i and 1 − i and 2.What are the images of the real and the imaginary axes? For i we have f(i)=(1+i)/(1-i) since i(depending on the power) can be i,-i,1,-1=>0, (1+i)/(1-i),(1-i)/(1+i) For 1 − i we have 1,-3,(2-i)/i,(2+i)/i. Not...

I'm sorry but that's how the problem is stated...f_k is defined to be f_k(x)=f(kx).

Sorry,f_k=f<sub>k sqrt= square root (Thinking)...is there something else?

I"m want to get a better understanding of the fourrier transform so I've started to do some problems. ^_f=fourrier transform of f. The function f belongs to the schwartz space and k>0 f_k(x)=f(kx). 1)show that f_k also belongs to the schwartz space and ^_f(e)=(1/k)^_f(e/k) 2)the fourrier...