"algebraic natural numbers" or "natural algebraic numbers" ?? At 08:12 PM 7/1/03 -0700, Marc LeBrun wrote:
=Jpr2718@aol.com
=Marc LeBrun <mlb@fxpt.com> Regarding Z*(SqrtD) = {x + y SqrtD; integer x, y, D>=0}... 2. What's best to call the whole algebraic structure?
For D squarefree and congruent to 2 or 3 modulo 4, it's the ring of algebraic integers of the field Q(\sqrt{D}) = {x + y \sqrt{D}; x and y rational}. [...]
Thanks for the informative answer. (Today I'm just looking at D=2, but this will help me later...)
Henry Baker also suggested "algebraic integer". However I objected on the grounds that x,y are restricted here to be non-negative. I thought "algebraic integer" connoted negative and even half-integer x&y. It also didn't seem right to say "ring" when there's no additive inverses.
Am I confused or just being obsessively pedantic about this? Thanks!