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If R is a ring and k is an element of Z, write kR = {kr | r is an element of R}. It is not too difficult to verify that {k is an element of Z | kR = 0} is an additive subgroup of Z.

I am confused on how kR would equal 0? Wouldn't that mean that k would have to equal zero? How could all of the elements of R multiplied by some integer k ever equal 0?

The book goes on to say that kR = 0 if and only if k1 = 0, where 1 = the unity of R.

Anyone want to help me understand what's going on here?