[FOM] Ring Theory/Question

Karim Zahidi karim.zahidi at ua.ac.be
Mon Jul 29 14:50:07 EDT 2013

I think that the answer to that question is negative. (I will suppose that R is a field, otherwise it is not entirely clear what R((lambda)) should be)
K can not be sandwiched in between R[lambda] and R[[lambda]] since the elements of the latter ring do not have poles at lambda=0 whereas K has elements with poles at lambda=0. 
K can not be sandwiched in between R[[lambda]] and R((lambda)), since the ring R[[lambda]] has elements which do not belong to K (e.g the element 1+lambda+lambda^2+lambda^3+....)

Op 29-jul-2013, om 14:56 heeft <pax0 at seznam.cz> <pax0 at seznam.cz> het volgende geschreven:

> Dear All,
> let R be a ring.
> It is obvious that the following inclusions hold
> R ⊆ R[lambda] ⊆ R[[lambda]] ⊆ R((lambda)).
> Here, R[lambda] is the ring of polynomials in the variable lambda,
> R[[lambda]] is the ring of formal power series over R,
> and R((lambda)) is the ring of Laurent series.
> Q. ***Can I put in general the quotient field K of R[lambda] somewhere in this chain?***
> Any justification is welcome.
> Jan Pax
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