If R and S are rings, the cartesian product RxS is a ring too with operations
(r1,s1) + (r2,s2) = (r1+r2,s1+s2)
(r1,s1)*(r2,s2) = (r1*r2,s1*s2)
0RxS = (0R,0s) 1RxS = (1R,1S)
and additive inverse -(r,s) = (-r,-s)
If R and S are nontrivial rings, show that RxS has at least 4 idempotent elements© BrainMass Inc. brainmass.com May 20, 2020, 7:44 pm ad1c9bdddf
Ring theory is clarified in this solution.