- #1
porroadventum
- 34
- 0
Homework Statement
Consider the ring Z/mZ, show that S = {[0], [a], [2a], · · · , [m − a]} forms a (possibly
nonunitary) subring of Z/mZ when a divides m. (i.e. show that (S,+, ·) is closed
the usual addition and multiplication. (We are not require to find a multiplicative identity).
The Attempt at a Solution
Since a divides m then m=ab so I tried subbing in ab for m and got [m-a]=[ab-a]=[a(1-b)]... but not too sure where to go from here. From looking at the set S it does not seem to be closed under addition or multiplication? Just a hint at how to go about/start/ approach this question would much appreciated! THank you!