Todd

Let Q(sqrt(2)) = { a + b*sqrt(2) | a and b are in Q}. Show that this set, with addition and multiplication, is a field.

Thank you!

Let a,b be nonzero integers with gcd(a, b)=1 , meaning reletively prime. compute gcd(a+b, a-b). thanks for any help. I was thinking to use Euclidean algorithm since it says to compute....

Let α:[-1,1] -->R² be the curve segment given by α(t)=(t, t²).

If φ=v² du + 2uv dv, compute the integral of φ over α.

compute

lim x->0 (x²sinx/sinx-xcosx)

were learning about L'hopitols rule, so it might be needed here.

Suppose that (S_n) is a sequence of real numbers. Show that if the absolute value of S_n converges to 0, then S_n converges to 0.

Also, Is it true that if absolute value of S_n converges to a>0, then S_n converges to a.

Prove a circular inversion is an onto transformation

Let R be the ring given by defining new operations on Z, by letting m*n=m+n-1 and let m**n=m+n-mn. define (Phi): from Z to R by

(Phi)(n)=1-n. show that (Phi) is an isomorphism.

NOTES: Phi is the greek letter Phi(looks like a circle with a verticle line through it. also (phi)(n) = phi of n. Z is the set of integers.

Thank you so much, I really need the help and explainations.

For the rings Zn and Zk, show that if k divides n then the function (Phi): Zn to Zk defined by Phi([Xn])=[X]k for all [X]n in Zn, is a ring homormorphism. show that this is the ONLY ring homomorphism from Zn to Zk.

Thanks for any help I really need it.

Notes: Zn means Z(sub n)= the set of integers subscript n. same for Xn and Xk and so on... also for [X]k, this means [X](sub k)

Also, Phi is the greek letter Phi, decsribing the ring.looks like a circle with a vertical line through it

Thank you, please be sure to explain how you got the answer also.

Define (Phi): Z to Zm * Zn by (Phi)(x)=([X]m,[X]n). find the kernel and image of (Phi) show that (Phi) is onto if and only if gcd(m,n)=1

Notes: Phi is the greek letter phi, looks like a circle with a vertical line through it. Z is the set of integers, Zn is Z(subscript n) same for the X's

Thanks so much for any help!

Pleae be sure to explain how you got the answer.

Define new operations on Q(the set of rational numbers) by letting a*b=a+b and a**b=2ab, for all a,b in Q. Show that Q is a commutative ring under these operations.

Please explain how to get the answer also.

Thanks for the help, its greatly needed and appreciated.

Define new operations on Q(the set of rational numbers) by letting a*b=a+b and a**b=2ab, for all a,b in Q. Show that Q is a commutative ring under these operations.

Please explain how to get the answer also.

Thanks for the help, its greatly needed and appreciated.

Abstract algebra- subgroups and cyclic generators?

let G=Z/<20> and H= <4>/<20> where H is a subgroup of G. List all elements of H and G/H.

WHats the answer?? and how do you get it??? thanks!

In words: let G= the set of intergers Z/the cyclic subgroup generated by 20 and H=cyclic subgroup generated by 4/ cyclic group generated by 20.

H is a subgroup of G. list elements of H and of G/H where G/H is the factor group of G determined by H.

I think it has somthing to do with cosets too?? Hope this helps to clarify a little. thanks for any help

let G=Z/<20> and H= <4>/<20> where H is a subgroup of G. List all elements of H and G/H.

WHats the answer?? and how do you get it??? thanks!

let G=Z/<20> and H= <4>/<20> where H is a subgroup of G. List all elements of H and G/H.

Let G={x in R ; x > 0 and x not equal to 1} define the operation * on G by a*b=a^(ln b), for all a,b in G. Prove that G is an abelian group under the operation *.