The algebraic unknotting number of a knot 
in 
is defined as the algebraic unknotting number of the 
-equivalence
class of a Seifert matrix of 
. The algebraic unknotting number of an element in an 
-equivalent
class is defined as the minimum number of algebraic unknotting operations necessary
to transform the element to the 
-equivalence class of the zero matrix (Saeki 1999).
Algebraic Unknotting Number
See also
Seifert Matrix, Unknotting NumberExplore with Wolfram|Alpha
References
Fogel, M. "Knots with Algebraic Unknotting Number One." Pacific J. Math. 163, 277-295, 1994.Murakami, H. "Algebraic Unknotting Operation, Q&A." Gen. Topology 8, 283-292, 1990.Saeki, O. "On Algebraic Unknotting Numbers of Knots." Tokyo J. Math. 22, 425-443, 1999.Referenced on Wolfram|Alpha
Algebraic Unknotting NumberCite this as:
Weisstein, Eric W. "Algebraic Unknotting Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AlgebraicUnknottingNumber.html