A Polynomial Composites and Monoid Domains as Algebraic Structures and their Applications

Magdalena Jankowska; Lukasz Matysiak

doi:10.34257/GJSFRFVOL21IS3PG71

A Polynomial Composites and Monoid Domains as Algebraic Structures and their Applications

Magdalena Jankowska * §

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Lukasz Matysiak

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Kazimierz Wielki University

A Polynomial Composites and Monoid Domains as Algebraic Structures and their Applications

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P91MC

DOI
10.34257/GJSFRFVOL21IS3PG71

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Abstract

This paper contains the results collected so far on polynomial composites in terms of many basic algebraic properties. Since it is a polynomial structure, results for monoid domains come in here and there. The second part of the paper contains the results of the relationship between the theory of polynomial composites, the Galois theory and the theory of nilpotents. The third part of this paper shows us some cryptosystems. We find generalizations of known ciphers taking into account the infinite alphabet and using simple algebraic methods. We also find two cryptosystems in which the structure of Dedekind rings resides, namely certain elements are equivalent to fractional ideals. Finally, we find the use of polynomial composites and monoid domains in cryptology.

References

16 Cites in Article

Reference Format

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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No ethics committee approval was required for this article type.

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How to Cite This Article

Magdalena Jankowska, Lukasz Matysiak. 2021. "A Polynomial Composites and Monoid Domains as Algebraic Structures and their Applications". Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 21 (GJSFR Volume 21 Issue F3).

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GJSFR Volume 21 Issue F3

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

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Classification

GJSFR-F Classification MSC 2010: 08A40

Submission ReceivedMay 12, 2021
Peer Review Double Blind
Handling Editor
Accepted June 3, 2021
Published June 15, 2021

Version of record

v1.2

Issue date

July 2, 2021

Language

English

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