On Zero Divided by Zero

In this study, we define the concept of inverse two operations and show that, i) Let  be a group, for all , then ii) Let  be a group,  such that  for all , then  for all  
iii) Let  be a ring,  such that  for all  then  for all
iv) Let , be an ordinary addition operation, be an ordinary multiplication, then  be a ring,  such that ,  be an inverse operation for , and     , i.e , for all .