Let a, b in R where R is a UFD.

Is it true that (a) intersects (b) = (c) always? Where (a),(b) and(c) are principal ideals

How do you prove it or give a counter-example?

Thank you for your time

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- Nov 12th 2009, 11:37 AMdangkhoaPrincipal ideals
Let a, b in R where R is a UFD.

Is it true that (a) intersects (b) = (c) always? Where (a),(b) and(c) are principal ideals

How do you prove it or give a counter-example?

Thank you for your time - Nov 12th 2009, 12:53 PMtonio
- Nov 12th 2009, 02:18 PMsignaldocPid <--> ufd ?
A PID is a UFD, but the converse requires more info. See (for example)

ftp://ftp.cis.upenn.edu/pub/papers/gallier/geomath3.pdf Proposition 5.40

All is not lost, I think. Here is a suggestion: Suppose a and b have common factor k: a=k*a1, b=k*b1. Then (I believe, and invite verification) the intersection of (a) and (b) is (k*a1*b1)=(c). This may require the ideal to be two sided.

Hope this helps....