As a general rule in mathematical notation, structures and collections are given uppercase names, while elements often have lowercase names. However, it's not uncommon for a field to be called $k$ (for example in this question). I know that this stands for the German word for field, Körper, but why lowercase?

  • 3
    $\begingroup$ Little $k$ for the small field, big $K$ for the big field (say, the function field of a variety over $k$)... $\endgroup$ – Zhen Lin Apr 2 '14 at 20:23
  • $\begingroup$ just a guess, but one extra ingredient in German was the prevalence of Fraktur for quite a while, still used for Lie algebras. Also, I always use upp er case for fields., so i think you are talking about specialists in some mathematics areas but not others. $\endgroup$ – Will Jagy Apr 2 '14 at 20:24
  • $\begingroup$ @WillJagy: yes, I deliberately said "not uncommon" rather than "usual". F and K seem to be at least as common as k. $\endgroup$ – Max Apr 2 '14 at 20:27
  • $\begingroup$ Just checked, Lam is consistent in always using upper case in Introduction to Quadratic Forms over Fields, AMS_GSM 67 (2004 or 2005). He uses a bar or a tilde or a dot directly over the letter to indicate related fields/things. Right, ~ is tilde, but Tilda Swinton. Also, PSG 3, Chelsea 1. $\endgroup$ – Will Jagy Apr 2 '14 at 20:32
  • 2
    $\begingroup$ @WillJagy, the second sentence of Chapter 1 of Hartshorne's Algebraic Geometry says, "We work over a fixed algebraically closed field $k$." Similarly, Section 2 of Chapter V in Weil's Basic Number Theory begins, "From now on, until the end of this Chapter, $k$ will denote an algebraic number-field." Lang also uses $k$ to denote a field in his book Algebra, but I can't locate where he first does so (the first appearance I could easily find is on page 162). $\endgroup$ – Barry Cipra Apr 2 '14 at 21:13

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.