is evidently also relatively integral; further the sum, difference and product of relative integral functions are themselves relatively integral.
The resulting problem is now to decide whether it is always possible to find a finite system of relatively integral function
by which every other relatively integral function of
may be expressed rationally and integrally.
We can formulate the problem still more simply if we introduce the idea of a finite field of integrality. By a finite field of integrality I mean a system of functions from which a finite number of functions can be chosen, in terms of which all other functions of the system are rationally and integrally expressible. Our problem amounts, then, to this: to show that all relatively integral functions of any given domain of rationality always constitute a finite field of integrality.
It naturally occurs to us also to refine the problem by restrictions drawn from number theory, by assuming the coefficients of the given functions
