Question 20277
 What is the meaning of F(x1,x2,...,xn)?
Please explain clearly with suitable example.


 What class you are studying ? You have to explain , there are no
 universal notations in some advanced math.

In general, F means a field x1,x2,..,xn means variables (not algebraic over F).

 F[x1,x2,...,xn] means the polynomial ring over F in the variables
 x1,x2,...,xn. (ie. poly. of variables x1,..,xn with coefficients in F)

 While F(x1,x2,...,xn) is the smallest field containing F[x1,x2,...,xn]
 (or called quotient field of F[x1,x2,...,xn]), which consists of
 all rational functions in x1,..,xn with coefficients in F.

 This question should belong to abstract algebra and you asked
 it in the wrong forum. I am the only person knowing what you talked
 about.

 Kenny