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Terminology of integers
Posted:
Aug 26, 2006 1:30 PM
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Certainly some people talk about "integers" in an algebraic function
field in the ring-theoretic sense -- algebraic functions that satisfy a
monic polynomial over the field of rational functions in one variable.
But I do not know how common this is.
For a translation of Emmy Noether's paper "Abstrakter Aufbau der
Idealtheorie" I need a term for "ganzen Grossen" in an algebraic
function field in that sense. This is the same term she uses for
integers in an algebraic number field. When she wants to specify
integers in the basic arithmetic sense, rational integers in algebraic
number fields, she uses "ganzen Zahlen."
A word-by-word translation would make "ganzen Grossen" into "integer
magnitudes." I have never heard anyone in English talk about "integer
magnitudes" in algebraic number fields. I think everyone just says
"integers." But is this also common in algebraic function fields?
Colin
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