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Functional composition and generalization of natural numbers by decomposition of semiring structure

12 July 2024, Version 2
Working Paper
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

We improve semiring composition of natural numbers to functional composition of them. From this functional composition, we select one generalization and see a specificity of natural numbers with proving a combinatorial theorem which derives fundamental identities.

Keywords

natural numbers
algebraic number theory
combinatorial number theory
divisor summatory function
arithmetic function

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Version History

Jul 12, 2024 Version 2

Version Notes

We have extensively added and corrected the content.

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License

All Rights Reserved

DOI

10.33774/coe-2024-7z62l-v2
D O I: 10.33774/coe-2024-7z62l-v2 [opens in a new tab]

Author’s competing interest statement

The author(s) have declared they have no conflict of interest with regard to this content

Ethics

The author(s) have declared ethics committee/IRB approval is not relevant to this content

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