--- Michael Reid <reid@math.ucf.edu> wrote:
... first consider p = 2 . note that
2A = { (a_n) in P | v(a_n) --> infinity and each a_n is even }
so there is an obvious countable basis for A/2A over Z/2Z , namely { e_i } , where e_i is 0 in all coordinates, except for a single 1 in the i-th coordinate. thus the dimension of A/2A over Z/2Z is countably infinite.
The e_i, regarded either as group generators or as a vector space basis, generate only finite sums, i.e. sequences that are 0 for all but finitely many coordinates. On the other hand, A/2A consists of arbitrary 0,1 sequences. Thus A/2A is uncountably infinite, and so its dimension over Z/2Z is also uncountably infinite. Gene __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com