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Complete Additivity, Complete Multiplicativity, and Leibniz-additivity on Rationals
Faculty of Information Technology and Communication Sciences, Tampere University, Tampere, Finland.
Faculty of Information Technology and Communication Sciences, Tampere University, Tampere, Finland.
Luleå University of Technology, Department of Health, Learning and Technology, Education, Language, and Teaching.ORCID iD: 0000-0002-7494-4632
2021 (English)In: Integers: Electronic Journal of Combinatorial Number Theory, E-ISSN 1553-1732, Vol. 21, article id A33Article in journal (Refereed) Published
Abstract [en]

Completely additive (c-additive in short) functions and completely multiplicative (c-multiplicative in short) functions are ordinarily defined for positive integers but sometimes on larger domains. We survey this matter by extending these functions first to nonzero integers and thereafter to nonzero rationals. Then we can similarly extend Leibniz-additive (L-additive in short) functions. (A function is L-additive if it is a product of a c-additive and a c-multiplicative function.) We study some properties of these functions. The role of an L-additive function as a generalized arithmetic derivative is our special interest.

Place, publisher, year, edition, pages
Colgate University , 2021. Vol. 21, article id A33
National Category
Other Mathematics
Research subject
Mathematics Education
Identifiers
URN: urn:nbn:se:ltu:diva-83393Scopus ID: 2-s2.0-85108210446OAI: oai:DiVA.org:ltu-83393DiVA, id: diva2:1539635
Note

Validerad;2021;Nivå 1;2021-03-26 (alebob)

Available from: 2021-03-24 Created: 2021-03-24 Last updated: 2023-10-03Bibliographically approved

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Scopushttp://math.colgate.edu/~integers/vol21.html

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Tossavainen, Timo

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