Notice the connection with the Euler indicator for the case where R = Z/mZ and R' = Z/nZ, with gcd(m,n) = 1.
The theorem gives 
(mn) =
(m) (n).
Notice the connection with the Euler indicator for the case where R = Z/mZ and R' = Z/nZ, with gcd(m,n) = 1.
The theorem gives (mn) =
(m) (n).