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 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 .

**References**

Rolfsen, D. *Knots and Links.* Wilmington, DE: Publish or Perish Press, pp. 206-207, 1976.

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1999-05-25