M�bius Categories as Reduced Standard Division Categories of Combinatorial Inverse Monoids

Lawvere intervals and the Möbius function of a Möbius category

“…Recently, Leinster [5], Lawvere and Menni [3] have brought attention to the problem of Möbius inversion in categories in a broader context. In previous papers [9]- [13], the first author of the present paper has found connections between the theory of combinatorial inverse semigroups and the theory of Möbius categories. The combinatorial inverse semigroups provide special examples of Möbius categories.…”

Derivations and generating degrees in the ring of arithmetical functions

“…In [9], they showed that A is a quasi-noetherian ring. Further results, in a more abstract categorical setting, have been obtained by Schwab in [6] and [7]. In [3], a class of absolute values and a family of derivations on the ring of arithmetical functions in several variables, with the analogue of Dirichlet convolution as multiplication, are defined and studied.…”

An algebraic independence result for Euler products of finite degree

“…Alkan and the authors [1] generalized this construction and provided a family of extensions of A r which are discrete valuation rings. For other work on rings of arithmetical functions the reader is referred to [5], [6], [9], [12], [13], [10], [11], [2]. In [1], it was shown that for any completely additive arithmetical function ψ ∈ A r , the map D ψ : A r → A r defined by D ψ (f )(n 1 , .…”