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Alexander Ideal

The order Ideal in $\Lambda$, the Ring of integral Laurent Polynomials, associated with an Alexander Matrix for a Knot $K$. Any generator of a principal Alexander ideal is called an Alexander Polynomial. Because the Alexander Invariant of a Tame Knot in ${\Bbb{S}}^3$ has a Square presentation Matrix, its Alexander ideal is Principal and it has an Alexander Polynomial $\Delta(t)$.

See also Alexander Invariant, Alexander Matrix, Alexander Polynomial


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

© 1996-9 Eric W. Weisstein