Unique factorization over fields/rings

  • Level: Graduate 
  • Thread starter Thread starter PsychonautQQ
  • Start date Start date
  • Tags Tags
    Factorization
Join the discussion
Registration is free. Start your own thread to ask a follow-up.
2 replies · 2K views
PsychonautQQ
Messages
781
Reaction score
10
Here is a direct quote from my textbook:
If R is a commutative ring, we say that a polynomial d in R[x] is a divisor of f in R[x] if f = qd for some q in F[x].

My question is did they mean to put q in F[x}? q isn't in R[x]? They didn't mention F[x] before this, is F[x] the field of all polynomials or something?
 
Physics news on Phys.org
PsychonautQQ said:
is F[x] the field of all polynomials or something?

To me, the "F[x]" looks like a typo that should be "R[x]" instead.
 
  • Like
Likes   Reactions: PsychonautQQ