Abstract
For each nz 1, let &,=e2ni’n and let O,=Z[[,,] be the ring of integers in the cyclotomic field K, of nth roots of unity. We denote 0, = li,m On = Un On the ring of all cyclotomic integers, the direct limit being taken with respect to the natural inclusions 0,-O, for n dividing m. For any commutative ring A, the group of isomorphism classes of projective modules of rank 1 is denoted by Pit(A) as usual. For instance, Pic(OJ is the ideal class group of On while Pic(Om) = lim Pic(OJ. The aim of this note is to prove the following plausible result which does not seem to be in the literature.
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