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## Main Question or Discussion Point

Hello Experts,

I post this question here because in the homework topics there is no abstract algebra!

Please help me I want to understand it:

I have a ring R with unit. Also I am given n - natural number, I_n is the set {x in R: n*x = 0}

I have to prove or refute: Given n, m natural numbers:

A) Is I_n + I_m is an ideal of the form of I_k?

B) Is I_n intersection with I_m is an ideal of the form of I_k?

C) Is I_n union with I_m is an ideal of the form of I_k?

I just used the Bezout's identity that d = ax+by for any d is a common devisor of a,b, and x,y are integers.

And I get that A is a proof.

For B I don't know how to start...

I post this question here because in the homework topics there is no abstract algebra!

Please help me I want to understand it:

I have a ring R with unit. Also I am given n - natural number, I_n is the set {x in R: n*x = 0}

I have to prove or refute: Given n, m natural numbers:

A) Is I_n + I_m is an ideal of the form of I_k?

B) Is I_n intersection with I_m is an ideal of the form of I_k?

C) Is I_n union with I_m is an ideal of the form of I_k?

I just used the Bezout's identity that d = ax+by for any d is a common devisor of a,b, and x,y are integers.

And I get that A is a proof.

For B I don't know how to start...