Addendum/Erratum for Arithmetic Duality Theorems
نویسنده
چکیده
Then H need not be divisible, i.e., we need not have pH D H . We only know H is contained in pG. Moreover, for x in H , there need not exist an infinite sequence y1;y2;y3:::: such that py2 D y1, py3 D y2; ::. We only know that there exist arbitrarily long finite such sequences. There does exist a unique maximal divisible subgroup D of M , and D is a subgroup of H . Moreover, M DD ̊N where N is a subgroup with no divisible subgroups and D is isomorphic to a direct sum of copies of Qp=Zp. Thus, unless there is some finiteness condition on M , you do have to worry about H being different from D. For example, M could have infinitely divisible elements but no divisible subgroup. For all this, see Kaplansky, Infinite Abelian Groups, University of Michigan Press, 1954.
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تاریخ انتشار 2014