Unique factorization over fields/rings

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The discussion centers on a quote from a textbook regarding polynomial division in commutative rings. The confusion arises from the notation used, specifically the mention of "q in F[x]" instead of "q in R[x]." Participants express skepticism about the accuracy of the notation, suggesting it may be a typo. The term "F[x]" is questioned, with some seeking clarification on whether it refers to a field of polynomials. Overall, the consensus leans towards the belief that "F[x]" should indeed be "R[x]."
PsychonautQQ
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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?
 
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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.
 
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i agree.
 
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I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...

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