Some formulas of varieties

[sanchop...@web.de]

Hello,

let R be a commutative ring with unit and I, J two ideals in R. I
think that I have figured out that the relation
V(I*J)=V(I/\J)=V(I) \/ V(J)
holds. Is this really true? I mean, the Chinese remainder theorem says
that I*J=I/\J if I+J=R and with the above relation one gets in any
case rad(I*J)=rad(I/\J) if R is a polynomial ring over an
algebraically closed field. Is the above equation really true?

Thanks,
S.

[Mariano Suárez-Alvarez]

On Jan 8, 7:24 pm, sanchopanch...@web.de wrote:
> Hello,
>
> let R be a commutative ring with unit and I, J two ideals in R. I
> think that I have figured out that the relation
> V(I*J)=V(I/\J)=V(I) \/ V(J)
> holds. Is this really true?

This is indeed true (assuming V(I) means what it usually means, of
course...)

-- m