The order ideal in , the ring of integral laurent polynomials, associated with an Alexander matrix for a knot. Any generator of a principal Alexander ideal is called an Alexander polynomial. Because the Alexander invariant of a tame knot in has a square presentation matrix, its Alexander ideal is principal and it has an Alexander polynomial.
, the ring of integral laurent polynomials, associated with an Alexander matrix for a knot 
. Any generator of a principal Alexander ideal is called an Alexander polynomial. Because the Alexander invariant of a tame knot in 
has a square presentation matrix, its Alexander ideal is principal and it has an Alexander polynomial 
.