The Alexander invariant 
of a knot 
is the homology of the infinite
cyclic cover of the complement of 
, considered as a module over 
, the ring
of integral laurent polynomials. The Alexander
invariant for a classical tame knot is finitely presentable,
and only 
is significant.
For any knot 
in 
whose complement has the homotopy type of a finite CW-complex, the Alexander invariant is finitely generated
and therefore finitely presentable. 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 denoted
.
