# Ring theory

1. Mar 1, 2008

### dash

Show that the set S = { 0, 4, 8, 12, 16, 24} is a subring of Z subscript 28. Then prove that the map Ø: Z subscript 7 → S given by Ø(x) = 8x mod 28 is an isomorphism

2. Mar 1, 2008

### quasar987

You need to show what you've tried before getting help.

3. Mar 2, 2008

### Hurkyl

Staff Emeritus
dash: The usual definition of the word "ring" requires it to have a multiplicative identity. Are you using the usual definition? Or are you using an alternate definition that doesn't make such a requirement?

It doesn't really matter for what you're actually trying to do -- but if you are using the usual definition of ring, then the subset {0, 4, 8, 12, 16, 24} of Z / 28 is a ring, but not a subring of Z / 28.