In Dummit and Foote Ch. 10 Introduction to Rings on page 228 we read:

"2Z is a subring of Z, as is nZ for any integer n. The ring Z/nZ is not a sub-ring (or a subgroup) of Z for any n $\displaystyle \geq $ 2."

Can anyone help me explictly prove that the ring Z/nZ is not a sub-ring (or a subgroup) of Z for any n >= 2.

Peter