Hello,
Isn't it k because of the characteristic of a field ? (just a thought, I have no idea if it's correct or not)
Often when one does field theory, or at least this was my experience, one's first encounter notationally with a field is that they are generically denoted or . This of course makes sense for the same reason that vector spaces are generically denoted , modules and monoids , rings , and groups . Moreover, it is common (in accordance with sets) that these structures should have a capitalized letter. That said, it seems to be a universal notation among more advanced field theory books (especially those dealing in algebraic number theory) to denote fields by --not f and not capitalized. Is there any particular reason for this? Is it possible that it is for the same reason that is the integer (zhalen)?
I think the answer lies in German, as with Zahlen for integers. The German word for field (in the algebraic sense) is Körper. Interestingly, the corresponding French word is corps, which (like Körper) means "body" in everyday usage.
Surprisingly, it seems to be very much more recent than that. The only online reference to the history of this notation that I have been able to find is here, where it is suggested that the first systematic use of Z for the integers and Q for the rationals is in Bourbaki's Algèbre. The Bourbaki group started work in the 1930s, but the first volume in the algebra series was not published until 1947. Before then, there does not seem to have been any standardised notation for number sets.