Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The problem is:

Show that every group and ring is congruence-permutable , but not necessarily congruence-distributive.

I know that in group every normal sub group has permutable property and in every ring , every ideal has permutable property. Moreover,for not being distributive I should give an example. please Guide me.

Thanks!

share|improve this question
    
What do "congruence-permutable" and "congruence-distributive" mean? –  Chris Eagle Jan 25 '13 at 10:44

1 Answer 1

If you compute the entire lattice of normal subgroups of the Klein 4-group, $\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}$, you will see you get the smallest modular non-distributive lattice, $M_3$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.