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- Abelian groups are a direct sum of cyclic groups. While this is true for finitely-generated abelian groups, it is far from true for infinitely-generated abelian groups, discount allegra no rx, Buy allegra online australia, even if you consider infinite direct sums. A typical infinitely-generated abelian group is Q, allegra online stores, Buying allegra, which cannot be written as a direct sum of any subgroups, but very much not cyclic.
- Finite-dimensional noncommutative division rings over the rationals are all subrings of the quaternions. The definition of the quaternions makes sense with coefficients in any subfield of the reals, order cheap allegra, Allegra side effects, and gives you a finite-dimensional division ring over that subfield. If the subfield is itself finite-dimensional over Q, this gives you a finite-dimensional division algebra over Q, allegra online without prescription. I thought that this construction gave you all of the possibilities, buy cheap allegra internet. Allegra pharmacy, This is far from the case. The quaternions are 4-dimensional over their center, buy discount allegra online, but you can construct other division algebras of any dimension over their center, as long as that dimension is a perfect square.
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