1. The problem statement, all variables and given/known data Let R be a ring in which 1_R = 0_R .Show that R has only one element. 2. Relevant equations 3. The attempt at a solution I'm trying to show that a*0_r=a*1_r implies a*0_r=0_r. if 0=0+0=>a*0=a*(0+0)=a*0+a*0=a*1_r+a*1_r=2a=>a*0=2a= >a=0....is this correct? If not Is there something I should do?