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 .
Alexander Ideal
See also
Alexander Invariant, Alexander Matrix, Alexander PolynomialExplore with Wolfram|Alpha
References
Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 206-207, 1976.Referenced on Wolfram|Alpha
Alexander IdealCite this as:
Weisstein, Eric W. "Alexander Ideal." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AlexanderIdeal.html