show ideal (X^5-Z^3, X^4-Y^3, Y^5-Z^4) in poly ring k[X,Y,Z]

[purple4reina]

My friend is working on his Ph.D. in math. He sent me this problem because he can't do it. Neither can anyone else in his class. I think he's freaking out about it..... Can anyone help?

Show the ideal (X^5-Z^3, X^4-Y^3, Y^5-Z^4) in the polynomial ring k[X,Y,Z] over an algebraically closed field cannot be generated by two elements

Thanks!

 

[mmm4444bot]

Re: Really hard question

... He sent me this problem because he can't do it ...

Hello Reina:

This approach toward getting help seems strange (to me) for a doctoral student. Are you his dissertation advisor?

i'm wondering if perhaps you're the one who's freaking ...

~ Mark :?

 

[Denis]

Re: Really hard question

Perhaps this would be helpful:

http://mathworld.wolfram.com/PolynomialRing.html

You'll see 3 links to try out!