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

Integral Domain, a^2=1

  • Thread starter Rederick
  • Start date
  • #1
12
0

Homework Statement



Let R be an integral domain with identity element 1. Show that there at most two elements "a" in R such that a^2=1


Homework Equations





The Attempt at a Solution



Being an integral domain implies that if ab=0, then a=0 or b=0. a^2=1 implies a=1. Then (a)(a) = (1)(1). This seems like a simple problem but I'm not sure how to properly state that there are "at most 2 elements."
 

Answers and Replies

  • #2
22,097
3,281
Saying that a2=1, is thesame as saying that a2-1=0. Maybe you can factorize the left hand side...
 
  • #3
12
0
Thank you. Got it
 

Related Threads on Integral Domain, a^2=1

Replies
5
Views
600
Replies
7
Views
2K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
15
Views
3K
Replies
8
Views
1K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
3
Views
445
Top