Let be a free Abelian Semigroup, where is the unit element, and let be the Möbius Function. Then do the following properties,

- 1. Implies for , where has the linear order ,
- 2. for all ,

for all ? The problem is known to be true for for all .

**References**

Flath, A. and Zulauf, A. ``Does the Möbius Function Determine Multiplicative Arithmetic?''
*Amer. Math. Monthly* **102**, 354-256, 1995.

© 1996-9

1999-05-26