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Arithmetical Functions and Distributivity

Published online by Cambridge University Press:  20 November 2018

P. J. McCarthy
P. J. McCarthy*
Affiliation:
University of Kansas, Lawrence, Kansas
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In this note we shall present a result about incidence functions on a locally finite partially ordered set, a result which is related to theorems of Lambek [2] and Subbarao [6]. Our terminology and notation will be that of Smith [4, 5] and Rota [7].

Let (L, ≤) be a partially ordered set which is locally finite in the sense that for all x, y ∊ L the interval [x, y] = {z | x ≤ z ≤ y} is finite. Denote by A(L, ≤) the set of functions f from L × L into some field, which is fixed once and for all, such that f(x, y) = 0 whenever x ≰ y.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 4 , December 1970 , pp. 491 - 496
Copyright
Copyright © Canadian Mathematical Society 1970

References

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