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- #1

- Jun 22, 2012

- 2,918

Note: (1) Two ideals A and B of the ring R are said to be comaximal if A + B = R

(2) Let I and J be two ideals of R

The sum of I and J is defined as [TEX] I+J = \{ a+b | a \in I, b \in J \} [/TEX]

- Thread starter Peter
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- Thread starter
- #1

- Jun 22, 2012

- 2,918

Note: (1) Two ideals A and B of the ring R are said to be comaximal if A + B = R

(2) Let I and J be two ideals of R

The sum of I and J is defined as [TEX] I+J = \{ a+b | a \in I, b \in J \} [/TEX]

- Thread starter
- #3

- Jun 22, 2012

- 2,918

Well ... I am still working on the problem ... but I will be using your guidance regarding the way to progress

At my day job at the moment ... but will use your hint when I return to the problem

Thanks again

Peter

- Jan 11, 2013

- 68

by def, two elements a,b in a PID are relatively prime if there exist, $m_1,m_2 \in $, such

that 1 = $m_1a+m_2b$

now if $a,b$ are relatively prime then

$\{r_1a + r_2b | r_1,r_2 \in R\}$, contains 1, if an ideal contains 1, then that ideal is identical to R.

Now <a> + <b> = $\{g_1a + g_2b | g_1,g_2 \in R\}$

that 1 = $m_1a+m_2b$

now if $a,b$ are relatively prime then

$\{r_1a + r_2b | r_1,r_2 \in R\}$, contains 1, if an ideal contains 1, then that ideal is identical to R.

Now <a> + <b> = $\{g_1a + g_2b | g_1,g_2 \in R\}$

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