Ring theory

  • Thread starter dash
  • Start date
7
0
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
 

quasar987

Science Advisor
Homework Helper
Gold Member
4,772
4
You need to show what you've tried before getting help.
 

Hurkyl

Staff Emeritus
Science Advisor
Gold Member
14,829
14
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.
 

Want to reply to this thread?

"Ring theory" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Top Threads

Top