Integral Domain, a^2=1

  • Thread starter Rederick
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  • #1
Rederick
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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."
 

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

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