1. The problem statement, all variables and given/known data Show that the intersection of any two subrings of a ring is a subring. 3. The attempt at a solution It seems abstract. suppose a+b=c and a*b=d Then if c is in A and B (where A and B are subrings) then the intersection of A and B denoted by C contains c and if C contains more the one element then it must contain a and b. My argument may not be general enough.