(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let I and J be ideals in R. Is the set K = {ab|a is an element of I, b is an element of J} an ideal in R?

2. Relevant equations

Conditions for an ideal, I of a ring R;

(i)I is nonempty,

(ii)for any c,e ε I: c-eεI

(iii)for any c ε I, rεR: rc, cr ε I.

3. The attempt at a solution

Let a,bεK.

K is not empty since it contains 0.

K seems to satisfy condition (iii) since r(ab)=(ra)b, and raεI since I is an ideal. Then (ra)bεK.

Also, (ab)r=a(br), and since brεJ, a(br)εK.

But nothing jumps out at me when I examine ab - cd , where a,cεI and b,dεJ.

Is it possible this is not an ideal?

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Proving an ideal in R.

**Physics Forums | Science Articles, Homework Help, Discussion**