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.

If you do, you may be part of the Fansons, and you probably know that Isaac is available, Taylor is married with a young baby boy, and Zac has a girlfriend.

The morale of the rank-and-file Highland railwaymen has remained remarkably high, in view of the extent to which the London press and many an English M.P. have already discarded their railways.

The raven is both a scavenger, who ravens a dead animal almost like a vulture, and a bird of prey, who commonly ravens to catch a rodent.