Möbius Problem
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 
.See also Braun's Conjecture, Möbius Function
References
Flath, A. and Zulauf, A. ``Does the Möbius Function Determine Multiplicative Arithmetic?'' Amer. Math. Monthly 102, 354-256, 1995.
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