I wanted to have example of group which can not be ring?

I think if we have non abelian group with some operation we can not proceed to ring . Is it correct or it required to more argument ?

Actually this question asked by my prof in class I answered same but he is not satisfied . so I was confused whether I am correct or not ?

Please give me suggestion .

  • 2
    $\begingroup$ Did your professor explain why he was not satisfied with your answer? Also, what exactly do you mean by "being made into a ring"? $\endgroup$
    – 5xum
    May 28, 2019 at 12:38
  • $\begingroup$ That means using any other possible operation (multiplication) . NO he just kept question open . And today he did not talk about that question $\endgroup$ May 28, 2019 at 12:43
  • $\begingroup$ Well clearly, just by adding multiplication, there is no way to change a non-abelian group into a ring. Your answer is perfectly fine... under one assumption. That assumption is that you correctly understood the question. $\endgroup$
    – 5xum
    May 28, 2019 at 12:45
  • $\begingroup$ You can take any existing ring $R$ and create a group ring $R[G]$ which are formal combinations of elements of the form $rg$ with $r \in R$ and $g \in G$.en.wikipedia.org/wiki/Group_ring $\endgroup$ May 28, 2019 at 12:46
  • $\begingroup$ Since the requirements for a ring include "abelian group with secondary operation that is associative" you need to specify that this group is also not associative, or find another non-qualifying property. The group in question could be non-abelian and then there could be some way for this to be the secondary operation for a ring. $\endgroup$
    – abiessu
    May 28, 2019 at 12:46