Abstract :
For every Dedekind domain R, Bhargava defined the factorials of a subset S of R by introducing the notion of -ordering of S, for every maximal ideal of R. We study the existence of simultaneous ordering in the case S=R=OK, where is the ring of integers of a function field K over a finite field . We show, that when is the ring of integers of an imaginary quadratic extension K of , , then there exists a simultaneous ordering if and only if degD 1.
