If $R$ is a UFD and $a,b \in R$ are relatively prime and $a|bc$, then $a|c$.
we know if a and b relatively prime (a,b)=1 so $a\bot b$. since $a|bc$ and $a\bot b$ doesn't $a$ has to divide $c$? I dont understand why do we need UFD?
If $R$ is a UFD and $a,b \in R$ are relatively prime and $a|bc$, then $a|c$.
we know if a and b relatively prime (a,b)=1 so $a\bot b$. since $a|bc$ and $a\bot b$ doesn't $a$ has to divide $c$? I dont understand why do we need UFD?