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Totally Multiplicative Functions in Regular Convolution Rings

Published online by Cambridge University Press:  20 November 2018

K. L. Yocom
K. L. Yocom*
Affiliation:
University of Wyoming, Laramie, Wyoming
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McCarthy [4] generalized a necessary and sufficient condition for an arithmetic function to be totally multiplicative to the incidence algebra on a partially ordered set. Several equivalent conditions for an arithmetic function to be totally multiplicative are known [1], [2]. In this paper we generalize several of these (and some apparently new ones) to the regular convolution rings of Narkiewicz [5]. We also investigate the prime factorization of arithmetic functions in a certain subring of some of these regular convolution rings.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 1 , March 1973 , pp. 119 - 128
Copyright
Copyright © Canadian Mathematical Society 1973

References

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