The M�bius Category of Some Combinatorial Inverse Semigroups

Schwab, Emil Daniel

doi:10.1007/s00233-004-0113-5

Cited by 11 publications

(7 citation statements)

References 6 publications

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“…The Theorem 2.3 suggests that the Möbius category C m arises from a combinatorial inverse semigroup. An examination of the Möbius function leads us to the free monogenic inverse monoid (see [10] , Proposition 3.3]). But C m is not the Möbius category (i.e.…”

Section: Final Remarksmentioning

confidence: 99%

Lawvere intervals and the Möbius function of a Möbius category

Schwab¹

2012

Discrete Mathematics and Applications

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Lawvere intervals of a Möbius category are finite one-way categories. We investigate a simple connection between the Möbius function of a Möbius category and the Möbius functions of its Lawvere intervals. In this investigation we have taken into consideration that a large class of Möbius categories arise as skeletons of division categories (that are right cancellative with pushouts). In general, the computation of the Möbius function for a Möbius category is laborious. In our case it becomes a routine computation on finite lattices. As an illustration, the results of this study may be used to compute the Möbius function of a proper Möbius category.

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Section: Final Remarksmentioning

confidence: 99%

Lawvere intervals and the Möbius function of a Möbius category

Schwab¹

2012

Discrete Mathematics and Applications

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“…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.…”

Section: Introductionmentioning

confidence: 98%

Derivations and generating degrees in the ring of arithmetical functions

Zaharescu

Zaki

2007

Proc Math Sci

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“…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 , .…”

Section: Introductionmentioning

confidence: 99%