# Thread: Finding an ideal to satisfy an algebraic variety

1. ## Finding an ideal to satisfy an algebraic variety

I am trying to find an ideal I <| K[x,y] such that the algebraic variety V(I) consists of:
.the point (1,1)
.the line x=0
.the line y= x+1

in A^2.

I do not understand how to do this.

Any help would be greatly appreciated.

2. Originally Posted by Siknature
I am trying to find an ideal I <| K[x,y] such that the algebraic variety V(I) consists of:
.the point (1,1)
.the line x=0
.the line y= x+1

in A^2.

I do not understand how to do this.

Any help would be greatly appreciated.

Try $I=<(x-1)(y-1),x,x-y+1>$ .

Tonio

3. Originally Posted by tonio
Try math]I=<(x-1)(y-1),x,x-y+1>[/tex] .

Tonio
Thankyou very much.

Should there be a comma between the (x-1) and (y-1) or is what you have written correct?