What's so big about that? I do it all the time.
We are now in a position to describe the subfield of K generated by F and our algebraic element u. This subfield F(u) clearly contains the subdomain F[u] of all elements expressible as polynomials f(u) with coefficients in F (cf. (1)). Actually, this domain F[u] is a subfield of K. Indeed, let us find an inverse for any element f(u) ≠ 0 in F[u]. … This shows that F[u] is a subfield of K. Since, conversely, every subfield of K which contains F and u evidently contains every polynomial f(u) in F[u], we see that F[u] is the subfield of K generated by F and u.
She could smell a faint aroma of machine oil and corflu emanating from the man cradling her worn (but not worn enough) form.
‘Them bloody chaps 'ave a cushy job,’ said little Martlow with resentful envy. ‘Just fly over the line, take a peek at ol' Fritz, and as soon as a bit o' shrapnel comes their way, fuck off 'ome jildy, toot suite.’
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