  The purpose of this paper is to give a new basis for examining the
relationships of the Affine Index Polynomial and the Sawollek Polynomial. Blake
Mellor has written a pioneering paper showing how the Affine Index Polynomial
may be extracted from the Sawollek Polynomial. The Affine Index Polynomial is
an elementary combinatorial invariant of virtual knots. The Sawollek polynomial
is a relative of the classical Alexander polynomial and is defined in terms of
a generalization of the Alexander module to virtual knots that derives from the
so-called Alexander Biquandle. The present paper constructs the groundwork for
a new approach to this relationship, and gives a concise proof of the basic
Theorem of Mellor extracting the Affine Index Polynomial from the Sawollek
Polynomial.
