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I just need someone to tell me if this is correct. If L and K are subfields of M, their composite LK is the smallest subfield of M that contains both L and K.

is this correct [tex]\alpha \in LK [/tex] if and only if there are positive integers n and m, polynomials [tex]f(x_1,x_2,...,x_n) \in L[x_1,...,x_n][/tex] and [tex]g(x_1,x_2,...,x_m) \in L[x_1,...,x_m][/tex], and elements [tex]a_1,...,a_n, b_1,...,b_m \in K[/tex] such that [tex]\alpha = \frac{f(a_1,...,a_n)}{g(b_1,...,b_m)}[/tex] ?

Thanks.

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# Composite of two fields

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