We introduce generic units in ZC(n) and prove that they are precisely the shifted cyclotomic polynomials. They generate the group Y(C-n) of constructible units. For each cyclic group we produce a basis of a finite index subgroup of integral units consisting of certain irreducible cyclotomic polynomials; this extends a result of Hoechsmann and Ritter. We also study 'alternating-like' units and decide when they generate a subgroup of finite index.
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