• Support PF! Buy your school textbooks, materials and every day products Here!

Show isomorphism

  • Thread starter stripes
  • Start date
  • #1
265
0

Homework Statement



Show that for any rings R and S, R x S and S x R are isomorphic, and A x B is the cartesian product, or ordered pairs. So an element of R x S can be written as (r1, s1).

Homework Equations





The Attempt at a Solution



So I have to show that there is a bijection from R x S to S x R, and this bijection must preserve addition and multiplication. This is tough for me since the mapping from R x S to S x R could be anything! How can I even start if I don't have this function or mapping?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
250
hi stripes! :smile:
… the mapping from R x S to S x R could be anything!
yes it could

but you're in charge, and you can choose any mapping you like :smile:

go for the "natural" mapping …

what do you think it would be really neat for (r1, s1) to be mapped onto? :wink:
 

Related Threads on Show isomorphism

  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
848
  • Last Post
Replies
2
Views
765
  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
3K
Replies
1
Views
401
Replies
8
Views
2K
Top