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

Calculating the characteristic of the cartesian product of rings

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

Homework Statement



See attached image
attachment.php?attachmentid=63020&stc=1&d=1381953319.jpg


Homework Equations





The Attempt at a Solution



For the first half of the question, ordered pairs would be (1, [1]), since 1 and [1] are the multiplicative identities in these rings. but no matter how many times we add (1, [1]) to itself, we'll never get (1, [1]) again. does this mean this ring has zero characteristic?
 

Attachments

Last edited:

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618

Homework Statement



See attached image
attachment.php?attachmentid=63020&stc=1&d=1381953319.jpg


Homework Equations





The Attempt at a Solution



For the first half of the question, ordered pairs would be (1, [1]), since 1 and [1] are the multiplicative identities in these rings. but no matter how many times we add (1, [1]) to itself, we'll never get (1, [1]) again. does this mean this ring has zero characteristic?
Yes, it has zero characteristic. What about the other ring?
 
  • #3
265
0
Other ring has characteristic 12, I hope.
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
Other ring has characteristic 12, I hope.
Sure it is, it's the least common multiple of 4 and 6.
 

Related Threads on Calculating the characteristic of the cartesian product of rings

Replies
1
Views
615
Replies
3
Views
2K
Replies
1
Views
3K
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
1
Views
3K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
4
Views
1K
Top