The square of a formal laurent series

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SUMMARY

The discussion centers on the properties of formal Laurent series in a field F, specifically addressing the condition where c equals f squared, with f being an element of F[[x]]. The user successfully demonstrates that if c = f^2, then f must belong to F, effectively eliminating terms with negative exponents and concluding with a formal power series. The user expresses gratitude for the community's support after resolving the query independently.

PREREQUISITES
  • Understanding of formal Laurent series and their properties
  • Familiarity with fields in abstract algebra
  • Knowledge of power series and their convergence
  • Basic experience with algebraic manipulations in F[[x]]
NEXT STEPS
  • Study the properties of formal power series in F[[x]]
  • Explore the implications of negative exponents in Laurent series
  • Investigate the relationship between fields and their power series
  • Learn about algebraic structures and their applications in formal series
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Mathematicians, algebraists, and students studying abstract algebra or formal series, particularly those interested in the properties of fields and power series.

R.P.F.
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Let [tex]F[/tex] be a field. Let [tex]c \in F[/tex].

I am trying to show that if
[tex]c = f^2[/tex] where [tex]f\in F[[x]][/tex], then [tex]f\in F[/tex].

So I am able to get rid of the terms with negative exponent. So now I'm left with a formal power series. Anyone knows how to do this? Thanks!
 
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Figured it out. So sorry, guys. :(
 

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