Let
be an Infinite Abelian Semigroup with linear order
such that
is the unit element and Implies for . Define a Möbius Function on by and
See also Möbius Problem
References
Flath, A. and Zulauf, A. ``Does the Möbius Function Determine Multiplicative Arithmetic?'' Amer. Math. Monthly 102, 354-256, 1995.