Recent content by lostinmath08

Thanks so much for your help!

i) (for all or any) x,y E R implies x+(-y) E R ii) (for all or any) x,y E R implies xy E R ( R is closed under mulitplication) so using the requirements of a subring...this is what i came up with: x-y=y-x -y-y=-x-x -2y=-2x y=x and vice versa. The above is just to satisfy the...

The following axioms must be satisfied a) (for all or any) x,y E R implies x+(-y) E R b) (for all or any) x,y E R implies xy E R ( R is closed under mulitplication) The above are the requirements for a subring to be valid. This is something i got from wikipedia: Let R be a ring. Any...

1. [B]The problem statement Let R be a ring. The center of R is defines as follows: Z(R)= {x E R where xy = yx for all y E R} Show that Z(R) is a subring of R The Attempt at a Solution I know that rings have to follow 4 axioms a) its an abelian group under addition b)...

1. [B]The Problem If S and T are subrings of a ring R, show that S intersects T, is a subring of R. The Attempt at a Solution I don't know how to go about answering this question.

I have already solved for the properties, but I thought the set matters.

Homework Statement On the set G=R-{1/3} the following operation is defined: *G: GxG arrow G (x,y) arrow x*y=x+y-3xy Show that (G,*) is an abelian group. Homework Equations To proove something is an abelian group: The Associative Law need to hold true x*(y*x)=(x*y)*x...

would it be wrong to use m, n and p? also the way i have presented the answer is it legitimate?

thank you!

Associative Law...help please..thanks! b1. Homework Statement [/b] On the set of real numbers R, the following is defined *:RxR arrow R (x,y) arrow x*y=a(x+y)-xy find all the values of the real parameter a such that the operation is associative Homework Equations associative...

i know where i made my mistake the first time, so e=1...im thinking. this is how i got to my second conclusion: 2(e+y)-ey-2=y 2e+2y-ey-2=y 2e-ey+2y-2=y e(2-y)=y-2y+2 e(2-y)=(2-y) e=(2-y)/(2-y) e=1 so my neutral element would be 1. thanks for the help!

[b]1. On the set of real numbers, R the following operation is defined: *RxR implies (arrow) R, (x,y) implies (arrow) x*y=2(x+y)-xy-2 Find the neutral element of this operation. [b]3. since we know x*e=x, e*x=x, so i attempted: using e as y, because it would just mean y...